Permeability estimation in tight and shale reservoirs is challenging because little or no flow will occur without hydraulic fracture stimulation. In the pressure falloff following a fracture calibration test (FCT), radial flow after the fracture closure can be used to estimate the reservoir permeability. However, for very low permeability, the time to reach radial flow can exceed any practical duration. This study shows how to use the reservoir pressure to estimate the maximum reservoir permeability when radial flow is missing in the after-closure response. The approach is straightforward and can also be used for buildup tests. It applies whenever the well completion geometry permits radial flow before the pressure response encounters a real well drainage limits. Recent developments have blurred the boundary between fracture calibration test analysis and classic pressure transient analysis. Adapting the log-log diagnostic plot representation to the FCT analysis has made it possible to perform before and after closure analysis on the same diagnostic plot. This paper also proposes a method for diagnosing abnormal leakoff behavior using the log-log diagnostic plot as an alternative method for the traditional G-function plot. The results show the relationship between reservoir permeability and pressure can be used effectively for both estimation of the permeability upper bound when there is no apparent radial flow and for confirming the permeability estimated from apparent late time radial flow. Numerous field examples illustrate this simple and powerful insight.

The aim of the diploma thesis is to clarify the topic of calibration samples used in eddy current testing on equipment in nuclear energy. The theoretical part of the diploma thesis is focused on the eddy current testing method, which belongs to the technology of non-destructive defectoscopy. This part of the work describes the principle of the method, its scope, limitations and dividing of sensors used in this test method. The work briefly describes the physical principle of the laser, its types and operating modes. The practical part of the work is focused on the production of a calibration samples by laser. Another point of the work is the comparison of data obtained from eddy current measurements on samples made by laser and on calibration samples used in practice.

違約機率校準檢定 - global test 由兩部分組成：第一部分為 level，探討真實的平均違約機率是否被高估；第二部分 shape，探討高低違約機率的表現情形。但 global test 與相關違約事件下的 level test 檢定尺度皆遠高於顯著水準 $\alpha$。本文先是針對相關違約事件，利用截斷分配使 level test 犯型一誤差機率更接近顯著水準，並提出虛無假設及對立假設為 $H_0: \theta \in \cup_{i=1}^2 \Theta_{i0}$ vs. $H_1: \theta \in \cap_{i=1}^2 \Theta_{i1}$ 的形式，引用交聯集檢定。更進一步透過 Liu \& Berger (1995, \textit{The Annals of Statistics}, 23, 1, 55-72) 建構齊一較強檢力檢定，改善檢定力。模擬結果顯示交聯集檢定與齊一較強檢力檢定的檢定尺度皆為 $\alpha$，且齊一較強檢力檢定的檢定力皆高於交聯集檢定。 / The calibration test of the PDs (probabilities of default) --- global test is twofold, the first part is the level test, which is about the mean of calibrated PDs. Second, the shape test is about whether a calibrated PD model differentiates correctly between low and high default probability events. In simulation results, we found that the type I error of global test is much greater than significant level $\alpha$, so is level test in correlation default events. In this study, firstly, we use the truncated level test to control previous error and suggest the hypothesis $H_0: \theta \in \cup_{i=1}^2 \Theta_{i0}$ vs. $H_1: \theta \in \cap_{i=1}^2 \Theta_{i1}$. Secondly, we introduce the intersection union test (IUT). Moreover, we construct an uniformly more powerful test (UMP test) by Liu \& Berger (1995, \textit{The Annals of Statistics}, 23, 1, 55-72). Simulation results show that the IUT and UMP test are size $\alpha$ tests, and the power of UMP test is greater than IUT.