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This work is concerned with the application of finite difference simulation to modelling the pressure response in partially penetrating oil wells. This has relevance to the oil and hydrology industries where pressure behaviour is used to infer the nature of aquifer or reservoir properties, particularly permeability. In the case of partially penetrating wells, the pressure response carries information regarding the magnitude of permeability in the vertical direction, a parameter that can be difficult to measure by other means and one that has a direct influence on both the total volumes of oil that can be recovered and on the rate of recovery. The derivation of the non-linear differential equations that form the basis for multiphase fluid flow in porous media is reviewed and it is shown how they can be converted into a set of finite difference equations. Techniques used to solve these equations are explained, with particular emphasis on the approach followed by the commercial simulation package used in this study. This involves use of Newton's method to linearize the equations followed by application of a pre-conditioned successive minimization technique to solve the resulting linear equations. Finite difference simulation is applied to a hypothetical problem of solving pressure response in a partially penetrating well in an homogenous but anisotropic medium and the results compared with those from analytical solutions. Differences between the results are resolved, demonstrating that the required level of accuracy can be achieved through selective use of sufficiently small grid blocks and time-steps. Residual discrepancies with some of the analytical methods can be traced to differences in the boundary conditions used in their derivation. The simulation method is applied to matching a complex real-life well test with vertical and lateral variation in properties (including fluid saturation). An accurate match can be achieved through judicious adjustment of the problem parameters with the proviso that the vertical permeability needs to be high. This suggests that the recovery mechanism in the oil field concerned can be expected to be highly efficient, something that has recently been confirmed by production results. / Thesis (M.Sc.)-University of Natal, Pietermaritzburg, 2002.

Thesis (MSc (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2007. / South Africa is involved in huge mining operations deep in the earth's crust. Stresses induced by these mining operations may cause seismic events or rockbursts to occur, which could damage infrastructure and put miners' lives at risk. The effect of different mining layouts are modelled and used by engineers to make design decisions. The frequency at which models are updated and integrated with the decision making process is not optimal. These large mining layouts can not be modelled adequately using domain methods, but they are particularly well suited for the boundary element method (BEM). This work focuses on the theory and background needed for creating a linear elastic static stress boundary element solver suited to South African mining layouts. It starts with linear elastic theory and subsequently describes the physical continuum, governing equations and the fundamental solutions which are an integral part of the BEM. Kelvin's solution cannot be applied to crack-like excavations, therefore the displacement discontinuity kernels, which are very well suited to model fractures, are derived. The derivation is approached from both the direct and indirect BEM's perspectives. The problem is cast as a boundary integral equation which can be solved using the BEM. Some of the different specializations of the BEM are discussed. The major drawback of the BEM is that it produces a dense influence matrix which quickly becomes intractable on desktop computers. Generally a mining layout requires a large amount of boundary elements, even for coarse discretization, therefore different techniques of representing the influence matrix are discussed, which, combined with an iterative solver like GMRES or Bi-CG, allows solving linear elastic static stress models.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Meteorology and Physical Oceanography, 1982. / Microfiche copy available in Archives and Science / Bibliography: leaves 108-109. / by Lawrence J. Pratt. / Ph.D.

Plant layout procedures available today consider either the quantitative attribute or the qualitative attribute of the layout problem. These procedures are based on maximizing or minimizing one objective function. Some of the procedures that address the multi-attribute nature of the plant layout problem are based on assigning weights to objective functions and then solving the problem by heuristic methods. Exact methods guarantee optimal solution but are computationally intensive for large sized problems. Heuristic methods do not guarantee optimal solution, but are computationally less intensive and relatively faster than the exact methods. This thesis suggests a procedure for solving the multi-attribute plant layout problem. The procedure is based on formulating the plant layout problem as a Quadratic Assignment Problem. Solution to the formulation is achieved by solving it by a combination of exact and heuristic methods. This solution procedure gives better results than just the heuristic method and is not computationally intensive. A computer implementation of the proposed procedure is developed in "C" programming language. A detailed experimentation is conducted to study the performance of the proposed procedure as compared to a well known procedure called Blocplan. The layouts generated by the proposed procedure are found to be much better than those generated by Blocplan. In the literature there is no discussion on the criticality of a layout to the change in flow related input data. An analysis is performed to study the affect of change in flow related input data on the final layout and a measure is developed for determining the criticality of a given layout to the change in flow related input data for the case of equal size departments. / M.S.

A fuel burnup model of a Pressurized Water Reactor (PWR) was developed based on one-group diffusion theory and used simple thermal cross sections. A computer program which simulates the depletion of the core of a PWR was written based on this model. The basic idea was to develop a fuel depletion program which could be readily understood by nuclear engineering students. Thus, accuracy was sacrificed for the sake of simplicity. The model was based upon a typical PWR with three concentric regions in the radial direction of differing fuel enrichment. Each of the regions was homogenized and the concentrations of the isotopes in each region were considered constant over a time interval. The isotopes considered were U-235, Pu-239, U-238, Xe-135, I-135, Sm-149, Pm-149 and the lumped burnable poison isotope. The flux was approximated by the sum of two trigonometric functions. The magnitude and shape of the flux were determined by holding power constant, constraining system to be critical and varying the soluble boron concentration to find the fla~test possible positive flux. A flux magnitude computed in this manner was compared to a similar flux magnitude given in a Final Safety Analysis Report. The concentrations of the isotopes were determined from the differential equations describing the rate of change of the concentrations. The behavior of the isotopes over core life was graphed and wherever possible compared to graphs from other sources. The concentrations calculated for U-235, U-238 and Pu-239 after 450 days were compared to the concentrations of the same isotopes calculated by a zero dimensional three-group model. The percentage difference between the concentrations determined by the two models varied from about 69% for Pu-239 to 1% for U-238. / Master of Science

published_or_final_version / Economics and Finance / Master / Master of Philosophy

We develop a dual-purpose damage model (DPDM) that can simultaneously model intralayer damage (ply failure) and interlayer damage (delamination) as an alternative to conventional practices that models ply failure by continuum damage mechanics (CDM) and delamination by cohesive elements. From purely computational point of view, if successful, the proposed approach will significantly reduce computational cost by eliminating the need for having double nodes at ply interfaces. At the core, DPDM is based on the regularized continuum damage mechanics approach with vectorial representation of damage and ellipsoidal damage surface. Shear correction factors are introduced to match the mixed mode fracture toughness of an analytical cohesive zone model. A predictor-corrector local-nonlocal regularization scheme, which treats intralayer portion of damage as nonlocal and interlayer damage as local, is developed and verified. Two variants of the DPDM are studied: a single- and two- scale DPDM. For the two-scale DPDM, reduced-order-homogenization (ROH) framework is employed with matrix phase modeled by the DPDM while the inclusion phase modeled by the CDM. The proposed DPDM is verified on several multi-layer laminates with various ply orientations including double-cantilever beam (DCB), end-notch-flexure (ENF), mixed-mode-bending (MMB), and three-point-bending (TPB). The simulation is executed in the platform of FOOF (Finite element solver based on Object-Oriented Fortran). The objective of FOOF is to develop a new architecture of the nonlinear multiphysics finite element code in object oriented Fortran environment. The salient features of FOOF are reusability, extensibility, and performance. Computational efficiency stems from the intrinsic optimization of numerical computing intrinsic to Fortran, while reusability and extensibility is inherited from the support of object-oriented programming style in Fortran 2003 and its later versions. The shortcomings of the object oriented style in Fortran 2003 (in comparison to C++) are alleviated by introducing the class hierarchy and by utilizing a multilevel programming style.

Bibliography: p. 474-514.

University of Macau / Faculty of Science and Technology / Department of Civil and Environmental Engineering