There have been many attempts to use mathematical method in order to characterize shale gas/oil reservoirs with multi-transverse hydraulic fractures horizontal well. Many authors have tried to come up with a suitable and practical mathematical model. To analyze the production data of a shale reservoir correctly, an understanding and choosing the proper mathematical model is required. Therefore, three models (the homogeneous linear flow model, the transient linear dual porosity model, and the fully transient linear triple porosity model) will be studied and compared to provide correct interpretation guidelines for these models. The analytical solutions and interpretation guidelines are developed in this work to interpret the production data of shale reservoirs effectively. Verification and derivation of asymptotic and associated equations from the Laplace space for dual porosity and triple porosity models are performed in order to generate analysis equations. Theories and practical applications of the three models (the homogeneous linear flow model, the dual porosity model, and the triple porosity model) are presented. A simplified triple porosity model with practical analytical solutions is proposed in order to reduce its complexity. This research provides the interpretation guidelines with various analysis equations for different flow periods or different physical properties. From theoretical and field examples of interpretation, the possible errors are presented. Finally, the three models are compared in a production analysis with the assumption of infinite conductivity of hydraulic fractures.

Orientador: Sérgio Kurokawa / Resumo: O objetivo deste projeto é desenvolver um modelo de linha de transmissão que leva em conta as principais características exigidas de um modelo deste componente do sistema elétrico, ou seja, ser desenvolvido diretamente no domínio do tempo, considerar que os parâmetros da linha são distribuídos ao longo de seu comprimento e levar em conta que os parâmetros longitudinais variam em função da frequência. O modelo proposto é baseado no modelo de Bergeron, que é um modelo de linha de transmissão desenvolvido diretamente no domínio do tempo e que leva em conta que os parâmetros de uma linha de transmissão são distribuídos ao longo de seu comprimento. No modelo proposto será levado em consideração que, devido aos efeitos solo e pelicular, os parâmetros longitudinais da linha (resistência longitudinal e indutância longitudinal) são variáveis em relação à frequência. Estes parâmetros serão aproximados por funções racionais e inseridos no modelo de Bergeron. O modelo desenvolvido será utilizado para representar linhas curtas e longas em simulações de transitórios eletromagnéticos resultantes de operações de manobras e de incidências de descargas atmosféricas. Por ser desenvolvido diretamente no domínio do tempo, o modelo proposto pode ser facilmente inserido em aplicativos do tipo ATP (Alternative Transients Program) e será uma ferramenta útil em simulações e análises de transitórios eletromagnéticos em sistemas de energia elétrica. / Abstract: The main objective of our project is to develop a transmission line model that takes into account the main characteristics demanded by a model of this electrical system component, i.e., be developed directly in the time-domain, consider the distributed nature of the line parameters and take into account the frequency dependence of the longitudinal parameters. The proposed model is based on the Bergeron model, which is a transmission line model directly developed in the time domain that takes into account that the transmission line parameters are distributed along its length. In the proposed model it will be taken into account that, due to earth-return effect and skin impedance, the longitudinal parameters (longitudinal resistance and longitudinal inductance) vary in relation to the frequency. These parameters will be approximated by rational functions and will be added to the Bergeron model. The developed model will be used to represent short and long transmission lines in simulations resulting from switching operations and lightning strikes. Because of the model being directly developed in the time-domain, the proposed model can be easily implemented in programs ATP-like (Alternative Transients Program) and will be a useful tool in power system transient analysis. / Doutor

Orientador: Antonio Carlos Bannwart / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica e Instituto de Geociencias / Made available in DSpace on 2018-08-15T14:50:36Z (GMT). No. of bitstreams: 1 Granzotto_DesireeGrenier_M.pdf: 5773051 bytes, checksum: 11febefe7b30f0680e59ad8a34976576 (MD5) Previous issue date: 2008 / Resumo: As grandes reservas mundiais de óleo pesado e os elevados preços do barril de petróleo tornam essencial o desenvolvimento de tecnologias de elevação e transporte desses óleos. O óleo pesado, com suas características desfavoráveis de alta viscosidade (100 - 10000 cP) e de densidade (abaixo de 20° API), necessita de métodos específicos que viabilizem sua movimentação em dutos a altas vazões. Para isto, um dos métodos mais simples e que não requer utilização de calor ou diluentes é oferecido pelo escoamento anular óleo-água (core-flow). Entre as questões ainda não resolvidas sobre esse escoamento está o controle do escoamento bifásico, de modo a se obter uma operação segura com a razão água-óleo adequada. Neste trabalho é apresentada uma modelagem do escoamento anular de óleo viscoso e água em regimes permanente e transiente no interior de um duto horizontal. Das possíveis estratégias de controle, optou-se, por simplicidade, pelo controle da vazão de água a uma dada vazão de óleo (desejada para a linha), através da atuação na rotação da bomba d'água. A modelagem permanente da perda de carga em escoamento anular foi ajustada aos dados experimentais colhidos em uma linha de aço de 2,5 polegadas de diâmetro nominal e comprimento 30 m, para diversas combinações de vazões de óleo e água, devido a certa aderência do óleo na parede do duto. A modelagem transiente satisfaz o critério clássico de estabilidade de Ledinegg. Esses resultados possibilitaram projetar e testar um sistema de controle para a vazão de água em duas versões: proporcional-integral (PI) e fuzzy. As comparações permitiram concluir pelo melhor desempenho do controlador fuzzy, por suas características e robustez / Abstract: The significant heavy oil reserves worldwide and the presently high crude oil prices make it essential the development of technologies for heavy oil production and transportation. Heavy oils, with their inherent features of high viscosity (100-10,000 cP) and density (below 22°API) require specific techniques for pipe flow at high flow rates. For this purpose, one of the simplest methods, which does not require use of heat or diluents, is provided by oil-water annular flow (core-flow). Among the still unsolved issues regarding core-flow is the two-phase flow control, in order to obtain a safe operation of the line at the lowest possible water-oil ratio. In this work a model of the viscous oil-water annular flow in a horizontal pipe for both steady and unsteady regimes is presented. From the possible strategies, the water flow rate control for a given oil flow rate was selected for simplicity. Due to the observation of some oil adherence to the wall, the steady state flow model was adjusted to experimental data collected in a 2.5 inches, 30 meters long steel pipe at several combinations of oil and water flow rates. On the other hand the transient model is shown to satisfy the well-known Ledinegg stability criterion. These features made it possible to design and testing a control system for the water flow rate in two different versions: proportional-integral (PI) and fuzzy. Comparisons indicate that the fuzzy controller performs better due to its features and robustness / Mestrado / Explotação / Mestre em Ciências e Engenharia de Petróleo

With the increase in energy consumption, new oil and gas extraction methods in unconventional resources have been explored. Hydraulic fracturing creates fractures to produce and make low permeability reservoirs economically profitable. Hydraulic fractures are also caused unintentionally by the uncontrolled injection in secondary recovery projects or CO2 geological storage. During proppant placement and CO2 injection, the permeability is reduced near the wellbore region due to pore clogging and mineral precipitation. The generated fractures act as high conductivity conduits that increase the capacity of flow in the reservoir. The fracture conductivity is strictly related to its geometry and hydraulic properties. However, these tend to degrade as pressure decreases. The current models do not consider fracture width change in the diffusivity inside the fracture. Additionally, the effect of fracture face skin in fracture closure has not been incorporated. This work focuses on the identification of fracture closure in fractured wells using Pressure Transient data. A semi-analytical model was developed for including the effects of fracture closure, fracture face skin, and complex fracture geometries. The matrix and fracture systems are coupled by pressure continuity at the interface. Fracture face skin is added, assuming a thin layer surrounding the fracture. The model is solved in Laplace space using a semi-analytical approach. The results are validated using a commercial simulator (CMG) and previous models. The pressure response in fractured wells with stress-sensitive fractures is analyzed at early, middle, and late times. In each time period, we identify pressure signals to detect fracture closure by incorporating effective fracture compressibility and fracture conductivity reduction. By incorporating the effective fracture compressibility, the model can reproduce a high storage capacity fracture signal. This signal occurs at early times and can help in post-fracture analysis. The fracture face skin creates an additional pressure drop in the fracture system, triggering conductivity reduction earlier than an undamaged fracture. We proposed a semi-log approach to identify fracture closure for slow rates of fracture closure and the pseudo-radial simplification to generate late time response curves instead of the complete solution for the model.

In this paper, we show how to utilize the expectation-maximization (EM) algorithm for efficient and numerical stable parameter estimation of the batch Markovian arrival process (BMAP). In fact, effective computational formulas for the E-step of the EM algorithm are presented, which utilize the well-known randomization technique and a stable calculation of Poisson jump probabilities. Moreover, we identify the BMAP as an analytically tractable model of choice for aggregated traffic modeling of IP networks. The key idea of this aggregated traffic model lies in customizing the BMAP such that different lengths of IP packets are represented by rewards of the BMAP. Using measured traffic data, a comparative study with the MMPP and the Poisson process illustrates the effectiveness of the customized BMAP for IP traffic modeling by visual inspection of sample paths over several time scales, by presenting important statistical properties as well as by investigations of queuing behavior.

This paper describes the analysis tool DSPNexpress which has been developed at the Technische Universität Berlin since 1991. The development of DSPNexpress has been motivated by the lack of a powerful software package for the numerical solution of deterministic and stochastic Petri nets (DSPNs) and the complexity requirements imposed by evaluating memory consistency models for multicomputer systems. The development of DSPNexpress has gained by the author's experience with the version 1.4 of the software package GreatSPN. However, opposed to GreatSPN, the software architecture of DSPNexpress is particularly tailored to the numerical evaluation of DSPNs. Furthermore, DSPNexpress contains a graphical interface running under the X11 window system. To the best of the author's knowledge, DSPNexpress is the first software package which contains an efficient numerical algorithm for computing steady-state solutions of DSPNs.

Time-domain methods are preferred over their frequency-domain counterparts for solving acoustic and electromagnetic scattering problems since they can produce wide- band data from a single simulation. Among the time-domain methods, time-domain surface integral equation solvers have recently found widespread use because they offer several benefits over differential equation solvers. This dissertation develops several second-kind surface integral equation solvers for analyzing transient acoustic scattering from rigid and penetrable objects and transient electromagnetic scattering from perfect electrically conducting and dielectric objects. For acoustically rigid, perfect electrically conducting, and dielectric scatterers, fully explicit marching-on-in-time schemes are developed for solving time domain Kirchhoff, magnetic field, and scalar potential integral equations, respectively. The unknown quantity (e.g., velocity potential, electric current, or scalar potential) on the scatterer surface is discretized using a higher-order method in space and Lagrange interpolation in time. The resulting system is cast in the form of an ordinary differen- tial equation and integrated in time using a predictor-corrector scheme to obtain the unknown expansion coefficients. The explicit scheme can use the same time step size as its implicit counterpart without sacrificing from the stability of the solution and is much faster under low-frequency excitation (i.e., for large time step size). In addition, low-frequency behavior of vector potential integral equations for perfect electrically conducting scatterers is also investigated in this dissertation. For acoustically penetrable scatterers, presence of spurious interior resonance modes in the solutions of two forms of time domain surface integral equations is investigated. Numerical results demonstrate that the solution of the form that is widely used in the literature is corrupted by the interior resonance modes. But, the amplitude of these modes in the time domain can be suppressed by increasing the accuracy of discretization especially in time. On the other hand, the proposed one in the combined form shows a resonance-free performance verified via numerical experiments. In addition to providing detailed formulations of these solvers, the dissertation presents numerical examples, which demonstrate the solvers’ accuracy, efficiency, and applicability in real-life scenarios.

This thesis presents the development of compact model of novel silicon carbide (SiC) Vertical Junction Field Effect Transistor (VJFET) for high-power circuit simulation. An empirical Angelov model is developed for SiC VJFET in PSpice. The model is capable of accurately replicating the device behavior for the DC and Transient conditions. The model was validated against measured data obtained from devices developed by Mississippi Center for Advanced Semiconductor Prototyping at MSU and SemiSouth Laboratories. The modeling approach is based on extracting Angelov Equations Coefficients from experimental device characteristics using non linear fitting. The coefficients are extracted for different parameters (temperature, width, etc). Multi-Dimensional Interpolation Technique is used to incorporate the effect of more than one parameter. The models developed in this research are expected to be valuable tools for electronic designers in the future. The developed model was applied for investigating the characteristics of a few standard analog circuit blocks using SiC VJFET and Si JFET in order to demonstrate the capabilities of the model to reveal the relative advantages of one over the other. The selected circuits of interest were Voltage Follower, Common Source Amplifier, Current Source and Differential Amplifier. Simulations of analog circuit building blocks incorporating SiC VJFET showed better circuit functionality compared to their Si counterparts.

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Electromagnetic transient and dynamic modeling and simulation studies are presented for a StatCom-SMES compensator in power systems. The transient study aims to better understand the transient process and interaction between a high power/high voltage SMES coil and its power electronics interface, dc-dc chopper. The chopper is used to attach the SMES coil to a StatCom. Following the transient study, the integration of a StatCom with SMES was explored to demonstrate the effectiveness of the combined compensator in damping power oscillations. The transient simulation package PSCAD/EMTDC has been used to perform the integrated modeling and simulation studies. A state of the art review of SMES technology was conducted. Its applications in power systems were discussed chronologically. The cost effective and feasible applications of this technology were identified. Incorporation of a SMES coil into an existing StatCom controller is one of the feasible applications, which can provide improved StatCom operation, and therefore much more flexible and controllable power system operation. The SMES coil with the following unique design characteristics of 50MW (96 MW peak), 100 MJ, 24 kV interface has been used in this study. As a consequence of the high power/ high voltage interface, special care needs to be taken with overvoltages that can stress the insulation of the coil. This requires an investigation of transient overvoltages through a detailed modeling of SMES and its power electronics interface. The electrical model for the SMES coil was developed based on geometrical dimensions of the coil. The interaction between the SMES coil and its power electronics interface (dc-dc chopper for the integration to StatCom) was modeled and simulated to identify transient overvoltages. Transient suppression schemes were developed to reduce these overvoltages. Among these are MOV implementation, surge capacitors, different configurations of the dc-dc chopper. The integration of the SMES coil to a StatCom controller was developed, and its dynamic behavior in damping oscillations following a three-phase fault was investigated through a number of simulation case studies. The results showed that the addition of energy storage to a StatCom controller can improve the StatCom-alone operation and can possibly reduce the MVA rating requirement for the StatCom operating alone. The effective location selection of a StatCom-SMES controller in a generic power system is also discussed. / Ph. D.