Methodology for Characterization of Scale Effects in Heterogeneous Subsurface flow system
Date Issued
2006
Date
2006
Author(s)
Wu, Cheng-Mau
DOI
zh-TW
Abstract
Spatial heterogeneity is ubiquitous in nature. Variability of parameter in subsurface is extensive. Researchers have devoted decades to seek a proper solution to represent the effective (or equivalent) parameters of heterogeneous media. The effective parameters are obtained by conceptualizing the heterogeneous soil formation as an equivalent homogeneous medium that will discharge approximately the same flux as the ensemble flux of the heterogeneous formations. This study explores solutions for the estimation of effective parameters in heterogeneous media first. Additionally, using wavelets as an analyzing tool, a solution for characterizing scale effects in heterogeneous subsurface porous media is proposed. The article is composed of two main parts:
(1) Estimations of effective parameter in heterogeneous media: Firstly, we clarify the concept of the effective parameter and address the problems of parameter estimation by traditional pumping test. Secondly, we present two estimation approaches (i.e., distance-drawdown and spatial moment analyses) for Seff and Teff, which are consistent with Theis' homogeneous aquifer assumption.
Results of estimation of effective parameters in heterogeneous show that: i) Seff and Teff values evolve with time, as well as the principal directions of the transmissivity; ii) Seff approaches the arithmetical mean of the field; iii) Teff converges to its geometric mean at large time for the Gaussian random field we generated; and iv) the averages of local T and S values within the cone of depression at early times differ from the Teff and Seff values. Both the averages and effective parameters, however, agree at large times, indicative of the existence of an REV in our domain if the pumping time is sufficiently long and there are no other effects (such as boundaries). At early time, estimated and values change with time, deviating significantly from the geometric means of the fields. The values stabilize rather quickly at the value dominated by the geology between the pumping and the observation well. At late times, values of approach but do not equal the geometric mean, and are influenced by the location, size, and degree of heterogeneity as the cone of depression evolves.
(2) Investigation and application of wavelet theory for characterization of scale effects in heterogeneous porous media. Three themes are explored: Firstly, by analogy to Fourier transform, we use a wavelet kernel function to derive the theoretical relationship between the wavelet spectrum of piezometric head and hydraulic conductivity in a one-dimensional heterogeneous system. Secondly, a homogenization process with wavelet multiresolution aspects is to determine the representative equivalent homogenized signal and to remove high frequency fluctuations under a specific threshold. Thirdly, we integrate wavelet multiresolution analysis with inverse problem to identify parameters with scale effect in heterogeneous media. An innovative parameter identification scheme is developed namely MRAIA (MultiResolution Analysis Inverse Algorithm), which combines wavelet multiresolution analysis (MRA), Gauss-Newton minimization scheme, and statistical test (AIC). Identify the structure and value of parameter properly and simultaneously.
The preliminary results show that wavelet based approaches have excellent achievement for homogenization and parameter identification. The potential exists for using wavelet analysis as the multiscale spatial heterogeneity analysis method for characterizing detailed geologic structures.
Subjects
異質性
參數化
尺度效應
有效參數
洩降-距離曲線分析
空間矩分析
小波多尺度分析
參數均一化
小波多尺度分析參數逆推演算法
AIC統計檢定法
heterogeneity
characterization
scale effects
effective parameter
distance-drawdown analyses
spatial moment analyses
wavelet multiresolution analysis
parameter homogenization
multiresolution analysis inverse algorithm
AIC test
Type
thesis
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