Mathematical Problems in Rock Mechanics and Rock Engineering

With increasing requirements for energy, resources and space, rock engineering projects are being constructed more often and are operated in large-scale environments with complex geology. Meanwhile, rock failures and rock instabilities occur more frequently, and severely threaten the safety and stability of rock engineering projects. It is well-recognized that rock has multi-scale structures and involves multi-scale fracture processes. Meanwhile, rocks are commonly subjected simultaneously to complex static stress and strong dynamic disturbance, providing a hotbed for the occurrence of rock failures. In addition, there are many multi-physics coupling processes in a rock mass. It is still difficult to understand these rock mechanics and characterize rock behavior during complex stress conditions, multi-physics processes, and multi-scale changes. Therefore, our understanding of rock mechanics and the prevention and control of failure and instability in rock engineering needs to be furthered. The primary aim of this Special Issue “Mathematical Problems in Rock Mechanics and Rock Engineering” is to bring together original research discussing innovative efforts regarding in situ observations, laboratory experiments and theoretical, numerical, and big-data-based methods to overcome the mathematical problems related to rock mechanics and rock engineering. It includes 12 manuscripts that illustrate the valuable efforts for addressing mathematical problems in rock mechanics and rock engineering

Hybrid Advanced Optimization Methods with Evolutionary Computation Techniques in Energy Forecasting

More accurate and precise energy demand forecasts are required when energy decisions are made in a competitive environment. Particularly in the Big Data era, forecasting models are always based on a complex function combination, and energy data are always complicated. Examples include seasonality, cyclicity, fluctuation, dynamic nonlinearity, and so on. These forecasting models have resulted in an over-reliance on the use of informal judgment and higher expenses when lacking the ability to determine data characteristics and patterns. The hybridization of optimization methods and superior evolutionary algorithms can provide important improvements via good parameter determinations in the optimization process, which is of great assistance to actions taken by energy decision-makers. This book aimed to attract researchers with an interest in the research areas described above. Specifically, it sought contributions to the development of any hybrid optimization methods (e.g., quadratic programming techniques, chaotic mapping, fuzzy inference theory, quantum computing, etc.) with advanced algorithms (e.g., genetic algorithms, ant colony optimization, particle swarm optimization algorithm, etc.) that have superior capabilities over the traditional optimization approaches to overcome some embedded drawbacks, and the application of these advanced hybrid approaches to significantly improve forecasting accuracy

Inversão sísmica bayesiana com modelagem a priori integrada com física de rocha

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas, Programa de Pós-Graduação em Física, Florianópolis, 2017.A inversão sísmica conjunta para as propriedades elásticas e petrofísicas é um problema inverso com solução não única. Existem vários fatores que afetam a precisão dos resultados como a relação estatística de física de rocha, os erros dos dados experimentais e de modelagem. Apresentamos uma metodologia para incorporar um modelo linearizado de física de rocha em uma distribuição Gaussiana multivariada. A proposta é usada para definir um modelo de mistura Gaussiana para a distribuiçãoconjunta a priori das propriedades elásticas e petrofísicas, no qual cada componente é interpretada como uma litofácies. Este processo permite introduzir uma correlação teórica entre as propriedades, com interpretação geológica específica dos parâmetros da física de rocha para cada fácies. Com base nesta modelagem a priori e no modelo convolucional, obtemos analiticamente as distribuições condicionais da amostragem de Gibbs. Em seguida, combinamos o algoritmo de amostragem com métodos de simulação geoestatística para obter a distribuição a posteriori de Bayes. Aplicamos a proposta em um conjunto de dados sísmicos reais, com três poços, para obter múltiplas realizações geoestatísticas tridimensionais das propriedades e das litofácies. A proposta é validada através de testes de poço cego e comparações com a inversão Bayesiana tradicional. Usando a probabilidade das litofácies, também calculamos a isosuperfície de probabilidade do reservatório de óleo principal do campo estudado. Além da proposta de inversão sísmica conjunta, apresentamos também uma formulação revisitada para o método de simulação geoestatística FFT-Moving Average. Nessa formulação, o filtro de correlação é derivado através de apenas um único ruído aleatório, o que permite a aplicação do método sem qualquer suposição sobre as características do ruído.Abstract : Joint seismic inversion for elastic and petrophysical properties is an inverse problem with a nonunique solution. There are several factors that affect the accuracy of the results such as the statistical rock-physics relation and observation errors. We present a general methodology to incorporate a linearized rock-physics model into a multivariate Gaussian distribution. The proposal is used to define a Gaussian mixture model for the joint prior distribution of the elastic and petrophysical properties, in which each component is interpreted as a lithofacies. This process allows to introduce a theoretical correlation between the properties with specific geological interpretation for the rock physicsparameters of each facies. Based on the prior model and on the convolutional model, we analytically obtain the conditional distributions of the Gibbs sampling. Then, we combine the sampling algorithm with geostatistical simulation methods to calculate the Bayesian posterior distribution. We applied the proposal to a real seismic data set with three wells to obtain multiple three-dimensional geostatistical simulations of the properties and the lithofacies. The proposal is validated through a blind well test and a comparison with the traditional Bayesian inversion. Using the probability of the reservoir lithofacies, we also calculated a 3D isosurface probability model of the main oil reservoir in the studied field