Prediction of rock and fluid properties such as porosity, clay content, and water saturation is essential for exploration and development of hydrocarbon reservoirs. Rock and fluid property maps obtained from such predictions can be used for optimal selection of well locations for reservoir development and production enhancement. Seismic data are usually the only source of information available throughout a field that can be used to predict the 3D distribution of properties with appropriate spatial resolution. The main challenge in inferring properties from seismic data is the ambiguous nature of geophysical information. Therefore, any estimate of rock and fluid property maps derived from seismic data must also represent its associated uncertainty. In this study we develop a computationally efficient mathematical technique based on neural networks to integrate measured data and a priori information in order to reduce the uncertainty in rock and fluid properties in a reservoir. The post inversion (a posteriori) information about rock and fluid properties are represented by the joint probability density function (PDF) of porosity, clay content, and water saturation. In this technique the a posteriori PDF is modeled by a weighted sum of Gaussian PDF’s. A so-called mixture density network (MDN) estimates the weights, mean vector, and covariance matrix of the Gaussians given any measured data set. We solve several inverse problems with the MDN and compare results with Monte Carlo (MC) sampling solution and show that the MDN inversion technique provides good estimate of the MC sampling solution. However, the computational cost of training and using the neural network is much lower than solution found by MC sampling (more than a factor of 104 in some cases). We also discuss the design, implementation, and training procedure of the MDN, and its limitations in estimating the solution of an inverse problem. In this thesis we focus on data from a deep offshore field in Africa. Our goal is to apply the MDN inversion technique to obtain maps of petrophysical properties (i.e., porosity, clay content, water saturation), and petrophysical facies from 3D seismic data. Petrophysical facies (i.e., non-reservoir, oil- and brine-saturated reservoir facies) are defined probabilistically based on geological information and values of the petrophysical parameters. First, we investigate the relationship (i.e., petrophysical forward function) between compressional- and shear-wave velocity and petrophysical parameters. The petrophysical forward function depends on different properties of rocks and varies from one rock type to another. Therefore, after acquisition of well logs or seismic data from a geological setting the petrophysical forward function must be calibrated with data and observations. The uncertainty of the petrophysical forward function comes from uncertainty in measurements and uncertainty about the type of facies. We present a method to construct the petrophysical forward function with its associated uncertainty from the both sources above. The results show that introducing uncertainty in facies improves the accuracy of the petrophysical forward function predictions. Then, we apply the MDN inversion method to solve four different petrophysical inverse problems. In particular, we invert P- and S-wave impedance logs for the joint PDF of porosity, clay content, and water saturation using a calibrated petrophysical forward function. Results show that posterior PDF of the model parameters provides reasonable estimates of measured well logs. Errors in the posterior PDF are mainly due to errors in the petrophysical forward function. Finally, we apply the MDN inversion method to predict 3D petrophysical properties from attributes of seismic data. In this application, the inversion objective is to estimate the joint PDF of porosity, clay content, and water saturation at each point in the reservoir, from the compressional- and shear-wave-impedance obtained from the inversion of AVO seismic data. Uncertainty in the a posteriori PDF of the model parameters are due to different sources such as variations in effective pressure, bulk modulus and density of hydrocarbon, uncertainty of the petrophysical forward function, and random noise in recorded data. Results show that the standard deviations of all model parameters are reduced after inversion, which shows that the inversion process provides information about all parameters. We also applied the result of the petrophysical inversion to estimate the 3D probability maps of non-reservoir facies, brine- and oil-saturated reservoir facies. The accuracy of the predicted oil-saturated facies at the well location is good, but due to errors in the petrophysical inversion the predicted non-reservoir and brine-saturated facies are ambiguous. Although the accuracy of results may vary due to different sources of error in different applications, the fast, probabilistic method of solving non-linear inverse problems developed in this study can be applied to invert well logs and large seismic data sets for petrophysical parameters in different applications.

Multiphase flows are of great interest to a large variety of industries because flows of two or more immiscible liquids are encountered in a diverse range of processes and equipment. However, the advent of high viscosity oil requires more investigations to enhance good design of transportation system and forestall its inherent production difficulties. Experimental and numerical studies were conducted on water-sand, oil-water and oilwater- sand respectively in 1-in ID 5m long horizontal pipe. The densities of CYL680 and CYL1000 oils employed are 917 and 916.2kg/m3 while their viscosities are 1.830 and 3.149Pa.s @ 25oC respectively. The solid-phase concentration ranged from 2.15e-04 to 10%v/v with mean diameter of 150micron and material density of 2650kg/m3. Experimentally, the observed flow patterns are Water Assist Annular (WA-ANN), Dispersed Oil in Water (DOW/OF), Oil Plug in Water (OPW/OF) with oil film on the wall and Water Plug in Oil (WPO). These configurations were obtained through visualisation, trend and the probability density function (PDF) of pressure signals along with the statistical moments. Injection of water to assist high viscosity oil transport reduced the pressure gradient by an order of magnitude. No significant differences were found between the gradients of oil-water and oil-water-sand, however, increase in sand concentration led to increase in the pressure losses in oil-water-sand flow. Numerically, Water Assist Annular (WA-ANN), Dispersed Oil in Water (DOW/OF), Oil Plug in Water (OPW/OF) with oil film on the wall, and Water Plug in Oil (WPO) flow pattern were successfully obtained by imposing a concentric inlet condition at the inlet of the horizontal pipe coupled with a newly developed turbulent kinetic energy budget equation coded as user defined function which was hooked up to the turbulence models. These modifications aided satisfactory predictions.

The estimation of probability density functions (PDF) of intensity values plays an important role in medical image analysis. Non-parametric PDF estimation methods have the advantage of generality in their application. The two most popular estimators in image analysis methods to perform the non-parametric PDF estimation task are the histogram and the kernel density estimator. But these popular estimators crucially need to be ‘tuned’ by setting a number of parameters and may be either computationally inefficient or need a large amount of training data. In this thesis, we critically analyse and further develop a recently proposed non-parametric PDF estimation method for signals, called the NP windows method. We propose three new algorithms to compute PDF estimates using the NP windows method. One of these algorithms, called the log-basis algorithm, provides an easier and faster way to compute the NP windows estimate, and allows us to compare the NP windows method with the two existing popular estimators. Results show that the NP windows method is fast and can estimate PDFs with a significantly smaller amount of training data. Moreover, it does not require any additional parameter settings. To demonstrate utility of the NP windows method in image analysis we consider its application to image segmentation. To do this, we first describe the distribution of intensity values in the image with a mixture of non-parametric distributions. We estimate these distributions using the NP windows method. We then use this novel mixture model to evolve curves with the well-known level set framework for image segmentation. We also take into account the partial volume effect that assumes importance in medical image analysis methods. In the final part of the thesis, we apply our non-parametric mixture model (NPMM) based level set segmentation framework to segment colorectal MR images. The segmentation of colorectal MR images is made challenging due to sparsity and ambiguity of features, presence of various artifacts, and complex anatomy of the region. We propose to use the monogenic signal (local energy, phase, and orientation) to overcome the first difficulty, and the NPMM to overcome the remaining two. Results are improved substantially on those that have been reported previously. We also present various ways to visualise clinically useful information obtained with our segmentations in a 3-dimensional manner.

We solve a random matrix ensemble called the chiral Ginibre orthogonal ensemble, or chGinOE. This non-Hermitian ensemble has applications to modelling particular low-energy limits of two-colour quantum chromo-dynamics (QCD). In particular, the matrices model the Dirac operator for quarks in the presence of a gluon gauge field of fixed topology, with an arbitrary number of flavours of virtual quarks and a non-zero quark chemical potential. We derive the joint probability density function (JPDF) of eigenvalues for this ensemble for finite matrix size N, which we then write in a factorised form. We then present two different methods for determining the correlation functions, resulting in compact expressions involving Pfaffians containing the associated kernel. We determine the microscopic large-N limits at strong and weak non-Hermiticity (required for physical applications) for both the real and complex eigenvalue densities. Various other properties of the ensemble are also investigated, including the skew-orthogonal polynomials and the fraction of eigenvalues that are real. A number of the techniques that we develop have more general applicability within random matrix theory, some of which we also explore in this thesis.

Statistical distributions also known as probability distributions are used to model a random experiment. Probability distributions consist of probability density functions (pdf) and cumulative density functions (cdf). Probability distributions are widely used in the area of engineering, actuarial science, computer science, biological science, physics, and other applicable areas of study. Statistics are used to draw conclusions about the population through probability models. Sample statistics such as the minimum, first quartile, median, third quartile, and maximum, referred to as the five-number summary, are examples of order statistics. The minimum and maximum observations are important in extreme value theory. This paper will focus on the probability distribution of the minimum observation, also known as the first order statistic, when the sample size is random.

IMRT uses non-uniform beam intensities within a radiation field to provide patient-specific dose shaping, resulting in a dose distribution that conforms tightly to the planning target volume (PTV). Unavoidable geometric uncertainty arising from patient repositioning and internal organ motion can lead to lower conformality index (CI), a decrease in tumor control probability (TCP) and an increase in normal tissue complication probability (NTCP). The CI of the IMRT plan depends heavily on steep dose gradients between the PTV and organ at risk (OAR). Geometric uncertainties reduce the planned dose gradients and result in a less steep or “blurred” dose gradient. The blurred dose gradients can be maximized by constraining the dose objective function in the static IMRT plan or by reducing geometric uncertainty during treatment with corrective verification imaging. Internal organ motion and setup error were evaluated simultaneously for 118 individual patients with implanted fiducials and MV electronic portal imaging (EPI). The Gaussian PDF is patient specific and group standard deviation (SD) should not be used for accurate treatment planning for individual patients. Frequent verification imaging should be employed in situations where geometric uncertainties are expected. The dose distribution including geometric uncertainties was determined from integration of the convolution of the static dose gradient with the PDF. Local maximum dose gradient (LMDG) was determined via optimization of dose objective function by manually adjusting DVH control points or selecting beam numbers and directions during IMRT treatment planning. EUDf is a useful QA parameter for interpreting the biological impact of geometric uncertainties on the static dose distribution. The EUDf has been used as the basis for the time-course NTCP evaluation in the thesis. Relative NTCP values are useful for comparative QA checking by normalizing known complications (e.g. reported in the RTOG studies) to specific DVH control points. For prostate cancer patients, rectal complications were evaluated from specific RTOG clinical trials and detailed evaluation of the treatment techniques. Treatment plans that did not meet DVH constraints represented additional complication risk. Geometric uncertainties improved or worsened rectal NTCP depending on individual internal organ motion within patient.

IMRT uses non-uniform beam intensities within a radiation field to provide patient-specific dose shaping, resulting in a dose distribution that conforms tightly to the planning target volume (PTV). Unavoidable geometric uncertainty arising from patient repositioning and internal organ motion can lead to lower conformality index (CI), a decrease in tumor control probability (TCP) and an increase in normal tissue complication probability (NTCP). The CI of the IMRT plan depends heavily on steep dose gradients between the PTV and organ at risk (OAR). Geometric uncertainties reduce the planned dose gradients and result in a less steep or “blurred” dose gradient. The blurred dose gradients can be maximized by constraining the dose objective function in the static IMRT plan or by reducing geometric uncertainty during treatment with corrective verification imaging. Internal organ motion and setup error were evaluated simultaneously for 118 individual patients with implanted fiducials and MV electronic portal imaging (EPI). The Gaussian PDF is patient specific and group standard deviation (SD) should not be used for accurate treatment planning for individual patients. Frequent verification imaging should be employed in situations where geometric uncertainties are expected. The dose distribution including geometric uncertainties was determined from integration of the convolution of the static dose gradient with the PDF. Local maximum dose gradient (LMDG) was determined via optimization of dose objective function by manually adjusting DVH control points or selecting beam numbers and directions during IMRT treatment planning. EUDf is a useful QA parameter for interpreting the biological impact of geometric uncertainties on the static dose distribution. The EUDf has been used as the basis for the time-course NTCP evaluation in the thesis. Relative NTCP values are useful for comparative QA checking by normalizing known complications (e.g. reported in the RTOG studies) to specific DVH control points. For prostate cancer patients, rectal complications were evaluated from specific RTOG clinical trials and detailed evaluation of the treatment techniques. Treatment plans that did not meet DVH constraints represented additional complication risk. Geometric uncertainties improved or worsened rectal NTCP depending on individual internal organ motion within patient.

IMRT uses non-uniform beam intensities within a radiation field to provide patient-specific dose shaping, resulting in a dose distribution that conforms tightly to the planning target volume (PTV). Unavoidable geometric uncertainty arising from patient repositioning and internal organ motion can lead to lower conformality index (CI), a decrease in tumor control probability (TCP) and an increase in normal tissue complication probability (NTCP). The CI of the IMRT plan depends heavily on steep dose gradients between the PTV and organ at risk (OAR). Geometric uncertainties reduce the planned dose gradients and result in a less steep or “blurred” dose gradient. The blurred dose gradients can be maximized by constraining the dose objective function in the static IMRT plan or by reducing geometric uncertainty during treatment with corrective verification imaging. Internal organ motion and setup error were evaluated simultaneously for 118 individual patients with implanted fiducials and MV electronic portal imaging (EPI). The Gaussian PDF is patient specific and group standard deviation (SD) should not be used for accurate treatment planning for individual patients. Frequent verification imaging should be employed in situations where geometric uncertainties are expected. The dose distribution including geometric uncertainties was determined from integration of the convolution of the static dose gradient with the PDF. Local maximum dose gradient (LMDG) was determined via optimization of dose objective function by manually adjusting DVH control points or selecting beam numbers and directions during IMRT treatment planning. EUDf is a useful QA parameter for interpreting the biological impact of geometric uncertainties on the static dose distribution. The EUDf has been used as the basis for the time-course NTCP evaluation in the thesis. Relative NTCP values are useful for comparative QA checking by normalizing known complications (e.g. reported in the RTOG studies) to specific DVH control points. For prostate cancer patients, rectal complications were evaluated from specific RTOG clinical trials and detailed evaluation of the treatment techniques. Treatment plans that did not meet DVH constraints represented additional complication risk. Geometric uncertainties improved or worsened rectal NTCP depending on individual internal organ motion within patient.

IMRT uses non-uniform beam intensities within a radiation field to provide patient-specific dose shaping, resulting in a dose distribution that conforms tightly to the planning target volume (PTV). Unavoidable geometric uncertainty arising from patient repositioning and internal organ motion can lead to lower conformality index (CI), a decrease in tumor control probability (TCP) and an increase in normal tissue complication probability (NTCP). The CI of the IMRT plan depends heavily on steep dose gradients between the PTV and organ at risk (OAR). Geometric uncertainties reduce the planned dose gradients and result in a less steep or “blurred” dose gradient. The blurred dose gradients can be maximized by constraining the dose objective function in the static IMRT plan or by reducing geometric uncertainty during treatment with corrective verification imaging. Internal organ motion and setup error were evaluated simultaneously for 118 individual patients with implanted fiducials and MV electronic portal imaging (EPI). The Gaussian PDF is patient specific and group standard deviation (SD) should not be used for accurate treatment planning for individual patients. Frequent verification imaging should be employed in situations where geometric uncertainties are expected. The dose distribution including geometric uncertainties was determined from integration of the convolution of the static dose gradient with the PDF. Local maximum dose gradient (LMDG) was determined via optimization of dose objective function by manually adjusting DVH control points or selecting beam numbers and directions during IMRT treatment planning. EUDf is a useful QA parameter for interpreting the biological impact of geometric uncertainties on the static dose distribution. The EUDf has been used as the basis for the time-course NTCP evaluation in the thesis. Relative NTCP values are useful for comparative QA checking by normalizing known complications (e.g. reported in the RTOG studies) to specific DVH control points. For prostate cancer patients, rectal complications were evaluated from specific RTOG clinical trials and detailed evaluation of the treatment techniques. Treatment plans that did not meet DVH constraints represented additional complication risk. Geometric uncertainties improved or worsened rectal NTCP depending on individual internal organ motion within patient.

Carbon dioxide (CO2) is the most important component of Greenhouse Gas (GHG) that causes global warming and sea-level rising. Thermal power plants dominate electric power generation in the world, and has been reported to be the major contributor of CO2 emission. To prevent the related global warming caused by GHG emission, carbon quota trading is implemented and becomes a gradually arising market. This thesis proposed a research focused on the relationship between the carbon trading scheme and dynamic economic dispatch (DED) problem for the public utility. A model of the carbon trading market was investigated and introduced into DED problem incorporating wind and solar power plant. A refined particle swarm optimization (PSO) algorithm, PSO with time-varying acceleration coefficients (PSO-TVAC), is applied to determine the DED strategy with the incorporation of independent power providers (IPPs) and green power plant. The model of the carbon trading was considered in the DED problem. Carbon reduction is treated as the inner-cost of utility, and the fictitious carbon quotas can be resold to the market, while the energy shortage can be satisfied by purchasing quotas from the market. In order to avoid premature convergence of the original PSO, the PSO-TVAC method is introduced to improve the searching efficiency.