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UBC Theses and Dissertations

The spatial filtering from core-scale conductivity to the conductivity measured by a slug test Wang, Bin


In the thesis, I investigate the measurement process of the slug test, an important and efficient engineering technique employed to probe aquifer properties. The objective is to determine the scale at which a slug test 'measures' hydraulic conductivity. To determine the scale, I conceptualize slug test measurement process in a system and filtering framework. I quantify, through numeric experiments, the spatial filtering effect of the slug test upon the core-scale hydraulic conductivity field. I examine the role of specific storage on this filtering effect. I develop two approaches to identify the system filter that epitomizes the filtering system — measurement process: spectral analysis with Wiener filtering and numerical perturbation. In heterogeneous media, system linearity is analyzed and the inverse estimation of the system output is evaluated. With the spectral approach, I optimally estimate the system filter in the presence of measurement noise. In homogeneous media where the spectral approach cannot be used, I apply the numerical perturbation approach. The spectral analysis and numerical perturbation are two conceptually different but complementary approaches. I analyze the nonparametric form of the system filter in heterogeneous media of various spatial variability and specific storage values. I determine the empirical parametric expression of equivalent filter width versus specific storage in homogeneous media. It is found that: 1. In both heterogeneous and homogeneous media, the equivalent filter width increases linearly with respect to log [mathematical formula which cannot be reproduced here; see pdf] 2. In homogeneous media, the filter amplitude decreases away from the wellbore by an approximate [mathematical formula which cannot be reproduced here; see pdf]. 3. A preliminary analysis of the role of heterogeneity characteristics upon the slugtest filtering was undertaken. The slug-test filtering was not strongly influenced by heterogeneity characteristics for log-conductivity variances less than 0.7. At variances less than 0.3, anisotropy in the conductivity field caused anisotropy in the slug-test filtering. These effects were not quantified in this thesis. In the end, I discuss the possible engineering and theoretical applications of the spatial filtering approach and make recommendations for future work.

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