One of the most important, but often ignored, factors affecting the transport and the seismic properties of hydrocarbon reservoir is pore shape. Transport properties depend on the dimensions, geometry, and distribution of pores and cracks. Knowledge of pore shape distribution is needed to explain the often-encountered complex interrelationship between seismic parameters (e.g. seismic velocity) and the independent physical properties (e.g. porosity) of hydrocarbon reservoirs. However, our knowledge of reservoir pore shape distribution is very limited. This dissertation employs a pore structure parameter via a rock physics model to characterize mean reservoir pore shape. The parameter was used to develop a new physical concept of critical clay content in the context of pore compressibility as a function of pore aspect ratio for a better understanding of seismic velocity as a function of porosity. This study makes use of well log dataset from offshore Norway and from North Viking Graben in the North Sea. In the studied North Sea reservoir, porosity and measured horizontal permeability was found to increase with increasing pore aspect ratio (PAR). PAR is relatively constant at 0.23 for volumes of clay (V_cl) less than 32% with a significant decrease to 0.04 for V_cl above 32%. The point of inflexion at 32% in the PAR –V_cl plane is defined as the critical clay volume. Much of the scatters in the compressional velocity-porosity cross-plots are observed where V_cl is above this critical value. For clay content higher than the critical value, Hertz-Mindlin (HM) contact theory over-predicts compressional velocity (V_p) by about 69%. This was reduced to 4% when PAR distribution was accounted for in the original HM formulation. The pore structure parameter was also used to study a fractured carbonate reservoir in the Sichuan basin, China. Using the parameter, the reservoir interval can be distinguished from those with no fracture. The former has a pore structure parameter value that is ≥ 3.8 whereas it was < 3.8 for the latter. This finding was consistent with the result of fracture analysis, which was based on FMI image. The results from this dissertation will find application in reservoir characterization as the industry target more complex, deeper, and unconventional reservoirs.

Radial basis function (RBF) approximation, is a new extremely powerful tool that is promising for high-dimensional problems, such as those arising from pricing of basket options using the Black-Scholes partial differential equation. The main problem for RBF methods have been ill-conditioning as the RBF shape parameter becomes small, corresponding to flat RBFs. This thesis employs a recently developed method called the RBF-QR method to reduce computational cost by improving the conditioning, thereby allowing for the use of a wider range of shape parameter values. Numerical experiments for the one-dimensional case are presented  and a MATLAB implementation is provided. In our thesis, the RBF-QR method performs better  than the RBF-Direct method for small shape parameters. Using Chebyshev points, instead of a standard uniform distribution, can increase the accuracy through clustering of the nodes towards the boundary. The least squares formulation for RBF methods is preferable to the collocation approach because it can result in smaller errors  for the same number of basis functions.

A series of pyridinium cationic lipids was designed, synthesized and characterized. These lipids varied in the lipophilic part, bearing C9 to C20 saturated, unsaturated, straight and branched hydrocarbon chains. The lipid shape parameter was calculated from the molecular structure of these lipids based on the partial molar volumes of the atoms, and standard bond lengths and bond angles, using fragment additive methods. The shape parameter controls the lamellar/hexagonal phase balance in lipoplexes of the lipid with deoxyribonucleic acid (DNA). The lipid phase behaviour of the lipoplexes was derived from small-angle X-ray scattering experiments and was successfully correlated with the calculated lipid shape parameter. The synthesized pyridinium lipids were co-formulated (1:1) with 1,2-dimyristoyl-sn-glycero-3-ethylphosphocholine (EPC) as the co-cationic lipid in 1:1 ratio, and the mixed cationic lipids were co-formulated (3:2) with the neutral lipids 1,2-dioleoyl-sn-glycero-3-phosphatidylethanolamine (DOPE) or cholesterol. The effect of variation in cationic lipid structure and lipoplex formulation on the transfection of nucleic acid (β-galactosidase and green fluorescent protein (GFP)) into CHO-K1 cells and the cytotoxicity of these formulations was assessed. Initial studies on the synthesized lipids bearing saturated and terminally unsaturated C16 chains showed that a Transfection Index (TIPSV) which encompasses the variation in the lipid shape parameter, the phase packing in a hexagonal lipoplex and the partition of these lipids into the lipoplex successfully correlated with transfection efficiency. To further investigate the effect of the variation of the partition of these lipids to the lipoplex, transfection studies were performed on a series of pyridinium lipids with straight saturated and unsaturated chains of varied lengths, with similar shape parameters but varied partition coefficients (clogP). The correlation of these experimental transfection data with the initial TIPSV was unsuccessful, but the data suggested that chain length as it relates to chain mixing and chain melting behaviours of pure lipids played a role in transfection. A refined transfection index (TIPSVM) was proposed which contained terms for the lipid shape parameter, the phase packing into a hexagonal lipoplex, the partition of these lipids into the lipoplex and a chain melting term. TIPSVM gave an acceptable correlation with the experimental transfection efficiency for the range of compounds. Additional experimental transfection data were obtained for compounds with widely variable lipid shape parameters, either as pure compounds, blends of two pure compounds, or statistically produced mixtures of mixed-chain compounds. Although very short-chain compounds (C9) and very lipophilic compounds (C20) performed poorly, the results from the blends allow the assessment of the role of the shape parameter in the TI. Since the shape parameter and the volume filling term are both calculated with the same molecular parameter, the experimental work demonstrated that only one of these terms is required. Thus a three parameter transfection index (TIPVM) was proposed and found to correlate with the entire set of comparable data. A Quantitative structure–activity relationship (QSAR) study was done on the cytotoxicity of the transfection formulations utilized. The toxicity of the synthesized pyridinium lipids was shown to correlate with the shape parameter, the lipid mixture partition co-efficient (clogP) and the charge ratio of the lipoplex formulation. Taken together, the developed transfection index TIPVM and the cytotoxicity correlation uncovered can be used in the design of low-toxicity, high activity pyridinium lipids for transfection of DNA. / Graduate / pariapz@uvic.ca

Calcareous shale, which is often encountered in construction projects, has a variety of physical and chemical properties that influence disintegration behavior of the rock mass. The diverse behavior of calcareous minerals in shale adds to the complexity of geotechnical investigations. Abundance of calcareous minerals is known to improve shale rock strength, although, when exposed to seasonal wetting and drying cycles, disintegration is rapid. The intent of this study is to statistically evaluate the disintegration behavior of calcareous shales in relation to their physico-chemical properties. Shale samples from fresh rock cuts and talus were tested using a multi-cycle slake durability index (Id), X-ray diffraction (XRD) analysis, scanning electron microscopy (SEM), energy-dispersive X-ray (EDX) elemental analysis, bulk density, natural water content, and porosity. A relationship was found between the degree of disintegration and the abundance of calcareous minerals, especially calcite and gypsum. Higher porosity and elevated water content were observed in highly weathered shales. Additionally, the efficiency of the Id test as an indicator of the degree of disintegration was evaluated. Grain-size distribution (GSD) analysis of disintegrated talus was compared with fragmental material of two-and five-cycle Id (Id2 and Id5) tests. The Coefficient of Uniformity (Cu) and Coefficient of Curvature (Cc) of Id5 materials showed satisfactory correlation with Cu and Cc of talus material. It is demonstrated that when compared to the conventional Id2 test, multi-cycle Id tests more precisely predict the disintegration pattern of shale and can be used to evaluate shale in terms of degree of disintegration.

O presente trabalho teve como meta desenvolver uma rotina computacional para obter a soluÃÃo numÃrica de equaÃÃes diferenciais parciais atravÃs do MÃtodo sem malhas. Esse mÃtodo vem sendo aplicado na engenharia, visto que nos casos prÃticos muitas vezes encontram-se descontinuidades ou condiÃÃes de contorno que impossibilitam a soluÃÃo analÃtica, e muitas vezes dificultam bastante as soluÃÃes numÃricas de equaÃÃes diferenciais parciais. No mÃtodo utilizado, calcula-se as equaÃÃes a partir do mÃtodo numÃrico de Kansa, onde toma-se uma FunÃÃo de Base Radial (RBF) que vai calcular a matriz a partir da qual chegaremos à soluÃÃo analÃtica. A RBF utilizada foi a multiquadrÃtica. Essa funÃÃo irà depender de um parÃmetro de forma âcâ. Esse parÃmetro nÃo tem um valor definido, e o objetivo da rotina à encontrar um valor para esse parÃmetro, de forma que a soluÃÃo analÃtica se aproxime o mÃximo possÃvel da soluÃÃo numÃrica. Para se calcular esse valor do âcâ, a rotina irà calcular os valores do resÃduo para o domÃnio, e os valores do resÃduo para o contorno, para cada valor de âcâ em um intervalo determinado. ApÃs calculados esses valores, o programa compara os mesmos e fornece o ponto em que eles se aproximam mais. Nesse ponto à encontrado o parÃmetro de forma âcâ otimizado, e consequentemente a soluÃÃo numÃrica da equaÃÃo proposta. / This study was aimed to develop a computational routine for the numerical solution of partial differential equations using the method without mesh. This method has been applied in engineering, since in practical cases often are discontinuities or boundary conditions that preclude the analytic solution, and often quite difficult numerical solutions of partial differential equations. In the method used, it is estimated the equations from the numerical method of Kansas, it takes it a Radial Basis Function (RBF) that will calculate the matrix from which will come to the analytical solution. The RBF used was multiquadrÃtica. This function will depend on a parameter in a "c". This parameter does not have a defined value, and the routine goal is to find a value for this parameter, so that the analytical solution is closely match the numerical solution. To calculate this value of "c", the routine will calculate the residue values &#8203;&#8203;for the domain, and the residue values &#8203;&#8203;for the outline, for each value of "c" in a certain range. After these calculated values, the program compares them and supplies the point where they are closer to. This point is found as the parameter "c" optimized, and therefore the numerical solution of the equation proposed.