Chemical kinetic investigation of a commercial batch reactor process

The aim of this investigation was to study the chemical reactions occurring during the batchwise production of a butylated melamine-formaldehyde resin, in order to optimise the efficiency and economics of the batch processes. The batch process models are largely empirical in nature as the reaction mechanism is unknown. The process chemistry and the commercial manufacturing method are described. A small scale system was established in glass and the ability to produce laboratory resins with the required quality was demonstrated, simulating the full scale plant. During further experiments the chemical reactions of methylolation, condensation and butylation were studied. The important process stages were identified and studied separately. The effects of variation of certain process parameters on the chemical reactions were also studied. A published model of methylolation was modified and used to simulate the methylolation stage. A major result of this project was the development of an indirect method for studying the condensation and butylation reactions occurring during the dehydration and acid reaction stages, as direct quantitative methods were not available. A mass balance method was devised for this purpose and used to collect experimental data. The reaction scheme was verified using this data. The reactions stages were simulated using an empirical model. This has revealed new information regarding the mechanism and kinetics of the reactions. Laboratory results were shown to be comparable with plant scale results. This work has improved the understanding of the batch process, which can be used to improve product consistency. Future work has been identified and recommended to produce an optimum process and plant design to reduce the batch time.

Calculating the balance between water resources and water demands:an approach using risk analysis

Predicting future need for water resources has traditionally been, at best, a crude mixture of art and science. This has prevented the evaluation of water need from being carried out in either a consistent or comprehensive manner. This inconsistent and somewhat arbitrary approach to water resources planning led to well publicised premature developments in the 1970's and 1980's but privatisation of the Water Industry, including creation of the Office of Water Services and the National Rivers Authority in 1989, turned the tide of resource planning to the point where funding of schemes and their justification by the Regulators could no longer be assumed. Furthermore, considerable areas of uncertainty were beginning to enter the debate and complicate the assessment It was also no longer appropriate to consider that contingencies would continue to lie solely on the demand side of the equation. An inability to calculate the balance between supply and demand may mean an inability to meet standards of service or, arguably worse, an excessive provision of water resources and excessive costs to customers. United Kingdom Water Industry Research limited (UKWlR) Headroom project in 1998 provided a simple methodology for the calculation of planning margins. This methodology, although well received, was not, however, accepted by the Regulators as a tool sufficient to promote resource development. This thesis begins by considering the history of water resource planning in the UK, moving on to discuss events following privatisation of the water industry post·1985. The mid section of the research forms the bulk of original work and provides a scoping exercise which reveals a catalogue of uncertainties prevalent within the supply-demand balance. Each of these uncertainties is considered in terms of materiality, scope, and whether it can be quantified within a risk analysis package. Many of the areas of uncertainty identified would merit further research. A workable, yet robust, methodology for evaluating the balance between water resources and water demands by using a spreadsheet based risk analysis package is presented. The technique involves statistical sampling and simulation such that samples are taken from input distributions on both the supply and demand side of the equation and the imbalance between supply and demand is calculated in the form of an output distribution. The percentiles of the output distribution represent different standards of service to the customer. The model allows dependencies between distributions to be considered, for improved uncertainties to be assessed and for the impact of uncertain solutions to any imbalance to be calculated directly. The method is considered a Significant leap forward in the field of water resource planning.

Fast reconstruction of harmonic functions from Cauchy data using the Dirichlet-to-Neumann map and integral equations

We propose and investigate a method for the stable determination of a harmonic function from knowledge of its value and its normal derivative on a part of the boundary of the (bounded) solution domain (Cauchy problem). We reformulate the Cauchy problem as an operator equation on the boundary using the Dirichlet-to-Neumann map. To discretize the obtained operator, we modify and employ a method denoted as Classic II given in [J. Helsing, Faster convergence and higher accuracy for the Dirichlet–Neumann map, J. Comput. Phys. 228 (2009), pp. 2578–2576, Section 3], which is based on Fredholm integral equations and Nyström discretization schemes. Then, for stability reasons, to solve the discretized integral equation we use the method of smoothing projection introduced in [J. Helsing and B.T. Johansson, Fast reconstruction of harmonic functions from Cauchy data using integral equation techniques, Inverse Probl. Sci. Eng. 18 (2010), pp. 381–399, Section 7], which makes it possible to solve the discretized operator equation in a stable way with minor computational cost and high accuracy. With this approach, for sufficiently smooth Cauchy data, the normal derivative can also be accurately computed on the part of the boundary where no data is initially given.

Fast reconstruction of harmonic functions from Cauchy data using integral equation techniques

We consider the problem of stable determination of a harmonic function from knowledge of the solution and its normal derivative on a part of the boundary of the (bounded) solution domain. The alternating method is a procedure to generate an approximation to the harmonic function from such Cauchy data and we investigate a numerical implementation of this procedure based on Fredholm integral equations and Nyström discretization schemes, which makes it possible to perform a large number of iterations (millions) with minor computational cost (seconds) and high accuracy. Moreover, the original problem is rewritten as a fixed point equation on the boundary, and various other direct regularization techniques are discussed to solve that equation. We also discuss how knowledge of the smoothness of the data can be used to further improve the accuracy. Numerical examples are presented showing that accurate approximations of both the solution and its normal derivative can be obtained with much less computational time than in previous works.

Direct sequence spread spectrum based PWM strategy for harmonic reduction and communication

Switched mode power supplies (SMPSs) are essential components in many applications, and electromagnetic interference is an important consideration in the SMPS design. Spread spectrum based PWM strategies have been used in SMPS designs to reduce the switching harmonics. This paper proposes a novel method to integrate a communication function into spread spectrum based PWM strategy without extra hardware costs. Direct sequence spread spectrum (DSSS) and phase shift keying (PSK) data modulation are employed to the PWM of the SMPS, so that it has reduced switching harmonics and the input and output power line voltage ripples contain data. A data demodulation algorithm has been developed for receivers, and code division multiple access (CDMA) concept is employed as communication method for a system with multiple SMPSs. The proposed method has been implemented in both Buck and Boost converters. The experimental results validated the proposed DSSS based PWM strategy for both harmonic reduction and communication.

Numerical solution of an elliptic 3-dimensional Cauchy problem by the alternating method and boundary integral equations

We consider the Cauchy problem for the Laplace equation in 3-dimensional doubly-connected domains, that is the reconstruction of a harmonic function from knowledge of the function values and normal derivative on the outer of two closed boundary surfaces. We employ the alternating iterative method, which is a regularizing procedure for the stable determination of the solution. In each iteration step, mixed boundary value problems are solved. The solution to each mixed problem is represented as a sum of two single-layer potentials giving two unknown densities (one for each of the two boundary surfaces) to determine; matching the given boundary data gives a system of boundary integral equations to be solved for the densities. For the discretisation, Weinert's method [24] is employed, which generates a Galerkin-type procedure for the numerical solution via rewriting the boundary integrals over the unit sphere and expanding the densities in terms of spherical harmonics. Numerical results are included as well.