Search results for: Yishan LIU

Authors: Serge Provost, Yishan Zang

Abstract:

Following a review of various approaches that are utilized for classifying the tail behavior of a distribution, an easily implementable methodology that relies on an arctangent transformation is presented. The classification criterion is actually based on the difference between two specific quantiles of the transformed distribution. The resulting categories enable one to classify distributional tails as distinctly short, short, nearly medium, medium, extended medium and somewhat long, providing that at least two moments exist. Distributions possessing a single moment are said to be long tailed while those failing to have any finite moments are classified as having an extremely long tail. Several illustrative examples will be presented.

Keywords: arctangent transformation, tail classification, heavy-tailed distributions, distributional moments

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Authors: Serge B. Provost, Yishan Zhang

Abstract:

A moment-based adjustment to the saddlepoint approximation is introduced in the context of density estimation. First applied to univariate distributions, this methodology is extended to the bivariate case. It then entails estimating the density function associated with each marginal distribution by means of the saddlepoint approximation and applying a bivariate adjustment to the product of the resulting density estimates. The connection to the distribution of empirical copulas will be pointed out. As well, a novel approach is proposed for estimating the support of distribution. As these results solely rely on sample moments and empirical cumulant-generating functions, they are particularly well suited for modeling massive data sets. Several illustrative applications will be presented.

Keywords: empirical cumulant-generating function, endpoints identification, saddlepoint approximation, sample moments, density estimation

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Authors: Serge Provost, Yishan Zang

Abstract:

Copulas are currently utilized in finance, reliability theory, machine learning, signal processing, geodesy, hydrology and biostatistics, among several other fields of scientific investigation. It follows from Sklar's theorem that the joint distribution function of a multidimensional random vector can be expressed in terms of its associated copula and marginals. Since marginal distributions can easily be determined by making use of a variety of techniques, we address the problem of securing the distribution of the copula. This will be done by using several approaches. For example, we will obtain bivariate least-squares approximations of the empirical copulas, modify the kernel density estimation technique and propose a criterion for selecting appropriate bandwidths, differentiate linearized empirical copulas, secure Bernstein polynomial approximations of suitable degrees, and apply a corollary to Sklar's result. Illustrative examples involving actual observations will be presented. The proposed methodologies will as well be applied to a sample generated from a known copula distribution in order to validate their effectiveness.

Keywords: copulas, Bernstein polynomial approximation, least-squares polynomial approximation, kernel density estimation, density approximation

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Authors: Chenqi Ge, Dongqi Ji, Yishan LIU, Zhengdong Lei, Zhangxing Chen, Gang Hui

Abstract:

Shale oil is the dominant contributor to global unconventional oil resource production. Compared to conventional oil and gas, shale oil productivity is significantly constrained by nano-confinement effects, which hinder oil flow from nano-pores (primary storage locations) to micro-fractures (main flow channels). Besides, the compact micro-fractures of low permeability cannot provide efficient flow channels to production well. These constraints result in inefficient oil displacement and fast production decline. Increasing temperature can simplify the phase change process and potentially enhance micro-fracture permeability by dilation. This study explores the potential of electrical heating enhanced shale oil flow by wind power transition, which can unlock the oil from tight shale oil formations. A non-isothermal numerical simulation approach is developed to model the thermal effects on shale oil flow dynamics. The model integrates nano-confined phase behavior, phase transition mechanics, multi-scale flow processes, heat transfer, and fracture dilation. A modified equation of state accounts for capillary pressure, adsorption, and nano-confinement. A coupled thermo-mechanical phase-field model simulates thermally induced micro-fractures. Model validation is performed by comparing simulation results against nano-scale experimental data. Further validation is conducted by the oil production performance comparison of simulation results and field history. Comparative analysis of the isothermal production method and electrical heating improvement approach in shale oil production confirm that elevated temperature improves oil phase consistency from nano-pores to fractures and increases micro-fracture permeability. As a result, oil flow is accelerated from tight formation to production well and thermal treatment makes a promising approach for shale oil production enhancement. Numerical simulation demonstrates that heat is primarily generated in the zone of high salinity saturation due to its high dielectric values. Meanwhile, the in-situ oil is simultaneously heated by conduction. Computation of energy efficiency provides that 100 % electric power can be transformed into heat in a shale oil formation by the ohm effect. Key results show that pore size dictates the target heating temperature, while shale mineral thermal expansion coefficients influence fracture initiation and dilation. Additionally, simulations indicate that a temperature increase of approximately 100°C significantly enhances shale oil mobility by improving phase change consistency from nano-pores to fractures and micro-fracture permeability. This study provides a computation framework for evaluating the effectiveness of thermal treatment in overcoming shale oil nano-confinement and compact fracture challenges.

Keywords: shale oil, thermally enhance oil recovery, nano-confinement, phase behavior, electric excitation

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