Steam Assisted Gravity Drainage (SAGD) is a commonly used EOR/IOR method for improving recovery in heavy oil reservoirs. However, continued research for a more energy efficient method has led to the development of an improved version called Expanding Solvent (ES)-SAGD, which has the potential to replace conventional SAGD method for production from some heavy oil reservoirs. This thesis provides some insights into determination of the reservoir performance of ES-SAGD process using an improved semi-analytical method. This model is then used for optimizing the solvent requirement while minimizing the steam injected. The semi-analytical model is determined by combining Butler’s oil drainage analytical model and solvent dilution effect of VAPEX process. The predictive ability of this model was improved by accounting for concentration and viscosity dependent solvent diffusion process. Results from this extended model in terms of solvent injection, oil production and Cumulative Steam to Oil Ratio (cSOR) were compared with that of reservoir simulation at various levels of grid resolution. Furthermore, the results from simulation were analyzed using response surface methodology including gradient based optimization technique to determine optimum operating conditions, which was then compared with more robust multi-objective optimization based on Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Pareto-optimality. Both the optimization techniques were used within the improved semi-analytical formulation to come up with optimized operational parameters. Modeling solvent diffusivity as a function of solvent concentration gives better results than those obtained using a constant value for diffusivity. Moreover, results for some key performance factors are in good agreement between the semi-analytical model and the numerical simulation, rendering this model suitable for performing solvents-screening studies. The multi-objective optimization framework within the semi-analytical model is demonstrated to be a feasible option for determining optimum ranges of key operating parameters that would result in success of the project. Intermediate values of solvent fraction ranging 0.1 to 0.2 for almost the entire range of injection pressures result in high bitumen recoveries and relatively low cSOR. The results indicate that higher values of solvent fraction at low operating pressures and lower values of solvent fraction at high operating pressures lead to optimized oil recovery rate and lower steam-oil-ratio. The multi-objective optimization process results in several combinations of control parameters that yield solutions along the Pareto-optimum front. These combinations are all viable solutions to the optimization problem. / text

The work in this thesis is focussed on obtaining fast, e cient solutions to the Schroedinger-Poisson model of electron states in microelectronic devices. The self-consistent solution of the coupled system of Schroedinger-Poisson equations poses many challenges. In particular, the three-dimensional solution is computationally intensive resulting in long simulation time, prohibitive memory requirements and considerable computer resources such as parallel processing and multi-core machines. Consequently, an approximate analytical solution for the coupled system of Schroedinger-Poisson equations is investigated. Details of the analytical techniques for the approximate solution are developed and the original approach is outlined. By introducing the hyperbolic secant and tangent functions with complex arguments, the coupled system of equations is transformed into one for which an approximate solution is much simpler to obtain. The method solves Schroedinger's equation rst by approximating the electrostatic potential in Poisson's equation and subsequently uses this solution to solve Poisson's equation. The complete iterative solution for the coupled system is obtained through implementation into Matlab. The semi-analytical method is robust and is applicable to one, two and three dimensional device architectures. It has been validated against alternative methods and experimental results reported in the literature and it shows improved simulation times for the class of coupled partial di erential equations and devices for which it was developed.

The life time of mechanical components can be increased by the presence of compressive residual stresses. Inherent to most production processes, residual stresses play a critical role on the mechanical parts behaviour. The knowledge and mastering of residual stresses and linked processes are thus fundamental. The development of efficient numerical methods to predict these residual stresses will allow to save costly experiments and to study the influence of the main parameters. This PhD presents the development and application of semi analytical methods (SAM) to the modelling of mechanical processes of compressive residual stress generation. The SAMs, initially developed for the simulation of elasto-plastic contacts, have the advantage of significantly low computation time compared to classical numerical methods. This method is first used to simulate the low plasticity burnishing process, with a rolling loading. Then, it is used for the simulation of impacts, first unique and then repeated. The frictionless rolling contact between two elasto-plastic bodies is first studied. The influence of plasticity, of the hardening model (isotropic or kinematic), of the geometry of the bodies in contact (spheres or ellipsoids) and of the loading type (indentation or rolling) on the contact pressure and plastic strains are analysed. Impacts simulation is then addressed. The developed method is first validated numerically then confronted to experimentations. Three materials have been particularly studied: 316L, AA 7010 and Inconel 600. The impacts dimensions and the generated strains, measured by digital image correlation, are used to validate experimentally the method. The ultrasonic shotpeening process has been specifically studied. The description of the kinematics of the shots put in movement by a sonotrode in a closed peening chamber has first been studied. The use of analytical formulae for the estimation of the coefficients of restitution, during the numerous impacts between shots and with the chamber's walls, allowed refining the calculation of the average impact velocity as a function of the process parameters. The SAM is the used to determine the plastic strain field induced by the impacts. At last a projection method is proposed to finally determine the residual stress field in thick or thin structures.

No / The advection–dispersion equation (ADE) is one of the most widely used methods for estimating natural stream pollution at different locations and times. In this paper, variational iteration method (VIM) is utilized to obtain a semianalytical solution for 1D ADE in a temporally dependent solute dispersion within uniformsteady flow. Through a computational validation, the effect of different parameters such as uniform flow velocity and dispersion coefficient on the solute concentration values has been investigated. Results show that the change in velocity has a strong effect on fluid density variation. However, when the diffusion coefficient has been increased, the change in flow and velocity behaviors is negligible. To verify the proposed semianalytical solution, the results were compared to analytical solutions and errors were found to be <0.7% in all simulations.

Anticipating how stream water quality will respond to change, such as increased pollution or water diversions, requires knowledge of the main mechanisms controlling water and chemical constituent movement and a reasonable representation of those mechanisms. By deriving mathematical models to represent a stream system and collecting supporting field-based measurements, water quality response can be predicted. However, because each stream is unique and the movement of water and constituents is spatially and temporally complex, assessing whether the stream is appropriately represented and whether predictions are trustworthy is still a challenge within the scientific and management communities. Building on decades of stream research, this dissertation provides a step towards better representing some of the complexities found within streams and rivers to better predict water quality responses over long stream distances. First, a method is presented to assess which mechanisms are considered most important in chemical constituent predictions. Next, the number of measurements necessary to represent the general complexities of water, mass, and heat movement in streams was determined. The advancements developed in this dissertation provide a foundation to more efficiently and accurately inform water resource management.

The majority of commercially available ultrasonic transducers used to excite and measure wave propagation in structures can be coupled only to a free surface. While convenient, this method is likely to excite multiple structural modes, making data interpretation difficult. Furthermore, the many modes excited make predicting the structure’s response a computationally intensive task. Here the dynamic radial displacement induced by a transient radial point load is calculated at more than 230,000 points on the outer surface of a virgin steel pipe to simulate a typical experiment. The radial component of the displacement field is calculated by convolving the Green’s functions of the pipe with the transient load. These functions are calculated on personal computers (in a distributed arrangement) by employing modal summation. The mode shapes are obtained from a Semi-Analytical Finite Element formulation used in conjunction with a separation of variables. The results are presented in a four dimensional animation, providing easier interpretations and insight into how to best select observation points for the detection of defects. The accuracy of the calculated displacements is verified experimentally. Agreement is good when magnitude and phase corrections are incorporated from the frequency response curves of the transducers used. / February 2005

Horizontal wells have been used to increase reservoir recovery, especially in unconventional reservoirs, and hydraulic fracturing has been applied to further extend the contact with the reservoir to increase the efficiency of development. In the past, many models, analytical or numerical, were developed to describe the flow behavior in horizontal wells with fractures. Source solution is one of the analytical/semi-analytical approaches. To solve fractured well problems, source methods were advanced from point sources to volumetric source, and pressure change inside fractures was considered in the volumetric source method. This study aims at developing a method that can predict horizontal well performance and the model can also be applied to horizontal wells with multiple fractures in complex natural fracture networks. The method solves the problem by superposing a series of slab sources under transient or pseudosteady-state flow conditions. The principle of the method comprises the calculation of semi-analytical response of a rectilinear reservoir with closed outer boundaries. A statistically assigned fracture network is used in the study to represent natural fractures based on the spacing between fractures and fracture geometry. The multiple dominating hydraulic fractures are then added to the natural fracture system to build the physical model of the problem. Each of the hydraulic fractures is connected to the horizontal wellbore, and the natural fractures are connected to the hydraulic fractures through the network description. Each fracture, natural or hydraulically induced, is treated as a series of slab sources. The analytical solution of superposed slab sources provides the base of the approach, and the overall flow from each fracture and the effect between the fractures are modeled by applying superposition principle to all of the fractures. It is assumed that hydraulic fractures are the main fractures that connect with the wellbore and the natural fractures are branching fractures which only connect with the main fractures. The fluid inside of the branch fractures flows into the main fractures, and the fluid of the main fracture from both the reservoir and the branch fractures flows to the wellbore. Predicting well performance in a complex fracture network system is extremely challenged. The statistical nature of natural fracture networks changes the flow characteristic from that of a single linear fracture. Simply using the single fracture model for individual fracture, and then adding the flow from each fracture for the network could introduce significant error. This study provides a semi-analytical approach to estimate well performance in a complex fracture network system.

At many sites it has become apparent that most chemicals of concern (COCs) in groundwater are persistent and not effectively treated by conventional remediation methods. In recent years, the permeable reactive barrier (PRB) technology has proven to be more cost-efficient in the long-run and capable of rapidly reducing COC concentrations by up to several orders of magnitude. In its simplest form, the PRB is a vertically emplaced rectangular porous medium in which impacted groundwater passively enters a narrow treatment zone. In the treatment zone dissolved COCs are rapidly degraded as they come in contact with the reactive material. As a result, the effluent groundwater contains significantly lower solute concentrations as it re-enters the aquifer and flows towards the plane of compliance (POC). Effective implementation of the PRB relies on accurate site characterization to identify the existing COCs, their interactions, and their required residence time in the PRB and aquifer. Ensuring adequate residence time in the PRB-aquifer system allows COCs to react longer, hence improving the probability that regulatory concentrations are achieved at the POC. In this study, the Park and Zhan solution technique is used to derive steady-state analytical and transient semi-analytical solutions to multispecies reactive transport in a permeable reactive barrier-aquifer (dual domain) system. The advantage of the dual domain model is that it can account for the potential existence of natural degradation in the aquifer, when designing the required PRB thickness. Also, like the single-species Park and Zhan solution, the solutions presented here were derived using the total mass flux (third-type) boundary condition in PRB-aquifer system. The study focuses primarily on the steady-state analytical solutions of the tetrachloroethylene (PCE) serial degradation pathway and secondly on the analytical solutions of the parallel degradation pathway. Lastly, the solutions in this study are not restricted solely to the PRB-aquifer model. They can also be applied to other types of dual domain systems with distinct flow and transport properties, and up to four other species reacting in serial or parallel degradation pathways. Although the solutions are long, the results of this study are novel in that the solutions provide improved modeling flexibility. For example: 1) every species can have unique first-order reaction rates and unique retardation factors, 2) higher order daughter species can be modeled solely as byproducts by neglecting their input concentrations, 3) entire segments of the parallel degradation pathway can be neglected depending on the desired degradation pathway model, and 4) converging multi-parent reactions can be modeled. As part of the study, separate Excel spreadsheet programs were created to facilitate prompt application of the steady-state analytical solutions, for both the serial and parallel degradation pathways. The spreadsheet programs are included as supplementary material.

The increasing concentration of CO_(2) has been linked to global warming and changes in climate. Geologic sequestration of CO_(2) in deep saline aquifers is a proposed greenhouse gas mitigation technology with potential to significantly reduce atmospheric emissions of CO_(2). Feasibility assessments of proposed sequestration sites require realistic and computationally efficient models to simulate the subsurface pressure response and monitor the injection process, and quantify the risks of leakage if there is any. This study investigates the possibility of obtaining closed form expressions for spatial distribution of CO_(2) injected in brine aquifers and gas reservoirs. Four new semi-analytical solutions for CO_(2) injection in brine aquifers and gas reservoirs are derived in this dissertation. Both infinite and closed domains are considered in the study. The first solution is an analysis of CO_(2) injection into an initially brine-filled infinite aquifer, exploiting self–similarity and matched asymptotic expansion. The second is an expanding to the first solution to account for CO_(2) injection into closed domains. The third and fourth solutions are analyzing the CO_(2) injection in infinite and closed gas reservoirs. The third and fourth solutions are derived using Laplace transform. The brine aquifer solutions accounted for both Darcyian and non-Darcyian flow, while, the gas reservoir solutions considered the gas compressibility variations with pressure changes. Existing analytical solutions assume injection under constant rate at the wellbore. This assumption is problematic because injection under constant rate is hard to maintain, especially for gases. The modeled injection processes in all aforementioned solutions are carried out under constant pressure injection at the wellbore (i.e. Dirichlet boundary condition). One major difficulty in developing an analytical or semi-analytical solution involving injection of CO_(2) under constant pressure is that the flux of CO_(2) at the wellbore is not known. The way to get around this obstacle is to solve for the pressure wave first as a function of flux, and then solve for the flux numerically, which is subsequently plugged back into the pressure formula to get a closed form solution of the pressure. While there is no simple equation for wellbore flux, our numerical solutions show that the evolution of flux is very close to a logarithmic decay with time. This is true for a large range of the reservoir and CO_(2) properties. The solution is not a formation specific, and thus is more general in nature than formation-specific empirical relationships. Additionally, the solution then can be used as the basis for designing and interpreting pressure tests to monitor the progress of CO_(2) injection process. Finally, the infinite domain solution is suitable to aquifers/reservoirs with large spatial extent and low permeability, while the closed domain solution is applicable to small aquifers/reservoirs with high permeability.

This thesis presents a theoretical study of thermoelastic guided waves in cylinders in the context of Lord-Shulman generalized theory of thermoelasticity. Two different methods were formulated to study dispersion relations in infinite cylinders. One of them is a Semi Analytical Finite Element (SAFE) method and the other is an analytical method. In the SAFE method, the dispersion equation has been formulated as a generalized eigenvalue problem by treating radial displacement and temperature with a one dimensional finite element model through the thickness of the cylinder. In the analytical method, displacement potentials are introduced to obtain the dispersion relations of guided wave modes. This method is applicable to isotropic cylinders and has been developed primarily to cross check the SAFE formulation. Frequency spectra obtained by both methods for an isotropic cylinder have shown excellent agreement with each other. Since the SAFE method can be used for an anisotropic composite cylinder, guided wave modes for anisotropic and composite cylinders are presented. Transient analysis of ultrasonic guided waves generated by concentrated heating of the outer surface of an infinite anisotropic cylinder has also been studied. The SAFE method is employed to model the response of a cylinder due to a pulsed laser focused on its surface. Green’s functions were constructed numerically by superposition of guided wave modes in frequency and wave number domains. Time histories of the propagating modes are then calculated by applying an inverse Fourier transformation in the time domain. Transient radial displacements of longitudinal and flexural modes of a silicon nitride cylinder are presented. Propagation of thermoelastic waves in finite length circular cylinders have also been investigated. The SAFE method is used to simulate the guided wave modes in the cylinder. Frequency spectra obtained by the SAFE formulation, for a finite length transversely isotropic cylinder, are validated by comparing the numerical results with relevant publications. Frequency spectra for axisymmetric and asymmetric modes in a silicon nitride finite cylinder with both ends insulated and restrained by frictionless rigid walls are presented. The plain strain problem of circumferential guided waves is also studied and the results are validated for an isothermal case.