<p>The velocity and concentration of slurries of closely-sized, spherical particles in water were measured at several locations in the dilute blanket of a laboratory-scale, continuous, thickener-clarifier. Particle velocities were measured by the laser Doppler technique; particle concentrations were measured by local scattered light intensity and by optical transmittance.</p> <p>Steady-state settling velocities as much as 70 percent higher than the average particle Stokes velocity occurred at slurry concentrations between 7.04 x 10‾² and 1.07 x 10ˉ¹ percent by volume. These findings contradicted all of the deterministic models commonly used to correlate slurry settling velocity with particle concentration. The failure of these models at dilute concentration was verified by flux measurements.</p> <p>The formation of clusters, whereby several particles settle as a group rather than individually, was used to explain the high velocities. Based on a binomial spatial distribution of particles, large clusters at concentrations slightly higher than the bulk solution concentration were predicted to occur with high probability.</p> <p>The few previous studies noting the formation of particle clusters were shown to have been dominated by wall effects at volumetric concentrations as low as 0.1 percent. The inverse variation of cluster size with slurry concentration accounted for the fact that the high velocities observed at low slurry concentrations have not been reported before.</p> <p>The results of this investigation have significant implications for optimizing the design and control of those unit operations and unit processes which depend on relative motion between particles and fluid.</p> / Doctor of Philosophy (PhD)

<p>Although several dynamic models of the nitrification process have been developed in recent years, application of this work to full scale design and operation has been limited. This is primarily due to the difficulties associated with accurate estimation of the several kinetic parameters required in these models. An examination of the literature indicated that differences in system SRT (Solids Retention Time) and influent carbon to nitrogen ratio (C:N) contribute to the wide diversity in reported nitrifier kinetics. This dissertation examines the degree to which these effects may be quantified for a combined carbon removal - nitrification process.</p> <p>A kinetic parameter, batch estimation technique was proposed which allows the measurement of nitrifier kinetics in the presence of heterotrophic microorganisms. The method utilizes a pure culture activity equivalent approach, and requires a specific nitrification inhibitor to differentiate between heterotrophic and autotrophic nitrogen dynamics measured in situ. This technique was found to give satisfactory results at several levels of nitrifier biomass fraction.</p> <p>The parameter estimation technique was then applied to laboratory scale extended aeration plants operated at a number of SRT and influent C:N levels. Parameter values determined under these conditions were summarized by empirical regression equations to quantify the SRT and C:N effects. Arrhenius temperature coefficients for pure nitrifiers at several SRTs were also determined.</p> <p>The equations relating SRT, C:N and temperature effects were then incorporated into a dynamic mechanistic model of the suspended growth carbon removal-nitrification process. Following verification against steady state and transient data from independent sources, it was concluded that the model adequately predicts mixed culture nitrification rates without prior parameter calibration.</p> <p>Several simulation runs were then utilized to illustrate that previously observed C:N effects were the result of altered nitrifier kinetics. However, reported SRT effects could be attributed to autotrophic-heterotrophic population dynamics.</p> / Doctor of Philosophy (PhD)

<p>This thesis deals with the different aspects of the successful application of size exclusion chromatography (SEC) for the molecular weight distribution (MWD) measurement of water soluble polymers. These aspects include methodology of mobile-phase development, selection of packing pore-sizes and methodology of molecular weight calibration and chromatogram interpretation. Qualitative understanding of ion-exclusion and adsorption, two of the more important and least understood complex phenomena in aqueous SEC was also provided.</p> <p>The polar nature and unique physical properties of water-soluble polymers in solution were found to be critically important in selection of mobile-phases and pore sizes. Due to the active sites present with most porous packing materials adequately suited for aqueous SEC application, adsorption, one of the resulting complications, was reduced preferentially, by addition of non-ionic surfactants such as Tergitol or polyethylene oxide to the mobile-phase. Ion-exclusion was controlled and reduced by addition of varying amounts of salt and/or acid to the mobile-phase. The optimal pH and ionic strength to the mobile-phase depended on the type of polymer being investigated. No common mobile-phase was found for the four polymers investigated (dextran, hydrolysed and non-hydrolysed polyacrylamide, and sodium polystyrene sulfonate).</p> <p>From viscosity data, these polymers were found to cover a very wide range of sizes in solution, with dextran being exceptionally very compact in solution when compared to polyacrylamide of the same molecular weight (MW). For this reason, selection of pore sizes was found to be critically important in achieving minimum peak broadening and maximum separation. Selection of one multi-column SEC system for general application to different water-soluble polymers was found not to be possible.</p> <p>Two powerful methods of molecular weight calibration, where simultaneously the peak broadening correction factors and the true molecular weight calibration curve are obtained, were developed. These methods require the use of multiple polydisperse MW standards, with known (Mn, Mw) or (Mn, [ƞ]). From these methods, a new shape of the instrumental spreading function was found. This was more general symmetric exponential type of spreading function provides a very simple definition of axial dispersion coefficient, which was shown not to be the most important fundamental parameter in SEC. With this shape function, apart from D2, the slope of the true MW calibration curve, the most important fundamental parameter (in the absence of skewing) was found to be the polyplatykurtic coefficient, its important increasing with increasing polydispersity of polymer samples.</p> / Doctor of Philosophy (PhD)

<p>In recent years, a number of chromatographic techniques have been reported to measure the size of submicron particles. Little of the published work has dealt with the quantitative estimation of particle size, efforts, largely, having been directed in demonstrating the capability to resolve colloid peaks. Ability to make quantitative measurements is a prime requirement for any analytical tool and this is the problem that is addressed in this work.</p> <p>Common to all the chromatographic techniques is the phenomenon of axial dispersion which disperses a colloid over a finite interval centered around its mean residence time or retention volume. The response to a pulse of monodispersed colloid is a bell shaped chromatogram, the shape of which along with the peak separation capability of the instrument, determine for a given detector, the type of analysis by which raw measured data have to be processed. The analysis may be of two types. The first, applies correction factors to moments calculated directly from the measured chromatogram to account for axial dispersion, while, the second approach allows a calculation of the moments of the diameter distribution of particles which at any instant occupy the detector cell. Besides developing the various methods for treating chromatographic data in detail, the problem of determining the response to a pulse of monodispersed colloid has been attempted. Experimentally, such information can be determined only with some difficulty, owing to the unavailability of very narrow distribution standards.</p> <p>Experiments were conducted using a size exclusion chromatograph equipped with a turbidity detector. The performance of the turbidity detector was critically evaluated. A column calibration procedure has been attempted which minimises material loss, significantly reduces the extent of axial dispersion and improves peak separation. The theoretical analyses discussed earlier were applied to experimental chromatograms of polystyrene latices with very encouraging results.</p> / Doctor of Philosophy (PhD)

<p>The overall objective of this program was to develop mathematical and experimental techniques, and thus obtain a mathematical model, capable of predicting the crystal size distribution as a function of batch time, for a seeded batch crystallizer in which alumina trihydrate was crystallizing in a supersaturated-aqueous solution of sodium aluminate.</p> <p>In this regard, a 2 bench-scale crystallizer was designed so as to operate in a similar way (with respect to mechanisms and rates) as industrial crystallizers in that gentle mixing allowed significant agglomeration to occur during the crystallization. Thus, nucleation, growth and agglomeration rates had to be predicted in the crystallizer model as a function of the crystallizer operation conditions.</p> <p>Reproduceable and representative samples were extracted from this crystalliser by a developed sampling system which did not contaminate or affect the sample nor the crystallizer contents. Analytical techniques were developed to obtain sodium aluminate and solids concentration. Crystal size distribution was measured for each sample by a special Coulter counter equipped with a Channelizer and a Log-Transformer apparatus. This equipment measured crystal volume with a resolution of 100 size intervals over a spherical equivalent diameter range of 4 to 80 μm. The lack of measurements below 4 μm was a source of trouble in the modeling program, and was the main source of error in the mathematical analyses using the particle size distribution data.</p> <p>A special mathematical method based on the population balance was developed to investigate and determine each of the rate equations for the processes growth, agglomeration, and nucleation individually from the obtained batch data. The method is termed here the method of pseudo moments'. It allows for investigation within feasible computer resources and circumvents the confounding of each of these processes with each other.</p> <p>The growth rate was modeled by a two-dimensional birth and spread mechanism, while the model for the agglomeration rate was based on a mechanism of free-in-space binary collisions with an agglomeration effectiveness kernel. This kernel was modeled by the product of a crystal environment term and a crystal size effect term. The form of the environment term suggests that the agglomeration rate is related to the growth rate lending support to the concept that alumina trihydrate crystals after collision are grown together to form true polycrystalline crystals and are not a 'flock' of crystals held together by physical attractive forces. The size-dependent term is made up of an inertial impaction mechanism term which accounts for the collision frequency, and a term which accounts for the efficiency of the collision. It was shown that crystals in the intermediate size range (ca. 10 to 30 μm) agglomerate most effectively. The expression for the nucleation rate, which was also developed using the pseudo-moment method suggests that the formation of nuclei in this experimental crystallizer at 85°C was not via normal homogeneous or heterogeneous nucleation mechanisms but rather occurred through attrition of very small particles from the seed particles (a sort of 'dusting-off' of nuclei-sized particles). These rate expressions still need to expanded for the effect of temperature, of intensity of agitation, and of impurities.</p> <p>Although the method of pseudo moments allows for the determination of rate expressions from size distribution data, it does not provide a means of predicting the evolution of size distributions. To this end a model based on the population balance, mass balances, and rate equations was formulated. However, such a model, if it includes agglomeration, is impractical for investigation of rate equations due to long numerical solution times.</p> <p>Because of the significance of the three rate processes the resulting model was made up of a set of algebraic equations and an integro-first order non-linear hyperbolic partial differential equation, with one of the integrals being a convolution integral. Numerical solution schemes of such an equation are prone to exhibit stability, accuracy, and long solution time problems. The stability and accuracy problems were solved and the long solution time problem minimized by the development of two numerical solution schemes. One was based on a developed weighted central difference approximation for the partial derivate with respect to crystal size and integrating by the Runge-Kutta Merson technique along a rectangular grid with respect to batch time. The other was based on solution along the characteristics of the equation and interpolating between the 'characteristic grid' and a specially developed rectangular grid for the integral terms. This grid allows for the convolution nature of one of the integrals. The resultant quadrature was fast and accurate. Depending on the type of crystallization process and the shape of the evolving size distribution either one or the other is best suited with regard to speed of solution and accuracy.</p> <p>The method of pseudo moments and numerical solution schemes allow for any growth, agglomeration, and nucleation expressions and any form of size distributions. Thus the numerical methods developed here for the determination of rate equations and prediction of size distributions are applicable to any particulate process, such as polymerization, microbial reactions, etc.</p> / Doctor of Philosophy (PhD)

<p>This thesis represents part of an ongoing study on the modelling and control of a pilot scale packed bed tubular reactor carrying out the hydrogenolysis of n-butane. The use of time series modelling and stochastic control to analyze and develop control strategies for this process was investigated.</p> <p>The mass and energy balances describing the hydrogenolysis of n-butane in this tubular reactor are a set of nonlinear partial differential equations in time and two spatial co-ordinates. In spite of their complexity, an analytical solution to these equations exists for certain linear combinations of the reaction species. These linear combinations, known as reaction invariants, define the reaction stoichiometry.</p> <p>A dynamic model of the process suitable for on-line computer control had previously been developed from the material and energy balances. This dynamic model, and a stochastic model for the inherent process disturbances, were used to investigate the optimal location of thermocouples along the central axis of the reactor. The results of this analysis indicated that good state estimation and control of the temperature profile, and effluent concentrations, could be achieved when one or two thermocouples were located in the vicinity of the hot spot (maximum) temperature. The location of the thermocouples was insensitive to the statistical properties of the disturbances. A canonical variate anlaysis of the reactor temperatures using this model indicated that the variation of the hot spot temperature and average temperature had significant predictable components. Other linear combinations of the axial temperatures were essentially white noise processes, and therefore unpredictable. Control of the hot spot temperature and average temperature would control most of the predictable variation in the temperature profile, and as a result, most of the predictable variation in the effluent concentrations.</p> <p>Univariate stochastic controllers designed for processes with deadtime have some very unusual spectral characteristics. The spectral characteristics of these controllers depend on the process deadtime and the structure and parameters of the stochastic disturbance model.</p> <p>A number of univariate self-tuning regulators were implemented to control the hot spot temperature. The self-tuning controller gave good control over the hot spot temperature when compared to digital propotional plus integral type controllers. This algorithm quickly tuned the controller parameters and was robust to the assumption in its derivation.</p> <p>Linear quadratic controllers designed for stochastic disturbance are identical to those designed to compensate for an 'equivalent' class of deterministic disturbances. When the controller structures are identical, it is the manner in which the state variables are reconstructed that determines how well a control strategy will perform. Although controllers can be readily designed to compensate process subject to deterministic and stochastic disturbances, reconstruction of the state variables in such instances is complicated by the presence of both type of disturbances.</p> / Doctor of Philosophy (PhD)

<p>The purpose of this research program was to investigate the void behaviour in a vertical conduit containing a flowing mixture of air and water.</p> <p>The local void fraction was measured by a neutron attenuation technique which was developed for this study. A neutron beam extracted from McMaster's 2MW Swimming Pool Nuclear Reactor was conditioned to provide a collimated beam of thermal neutrons with low gamma and fast neutron back-ground. An atmospheric vertical upward cocurrent air-water loop was constructed in front of the beam port.</p> <p>A series of experiments was performed to obtain information on the steady-state radial void profile in the bubbly and annular flow regimes for a 3/4 in. I.D. test section with gas and liquid volumetric fluxes up to about 32 m/sec and 80 cm/sec, respectively. The dynamic behaviour of the system to a perturbation in gas flowrate was measured and compared to that predicted by the void propagation equation.</p> <p>The adequacy of the netron attenuation method for radial void profile measurements in two-phase flow was ascertained. This was achieved by integrating the measured radial void profile and comparing the resulting cross-sectional average void fraction with that obtained by a trapping method. The neutron attenuation method was also shown to be an excellent tool for flow regime recognition and for testing the flow development. The effect of the statistical fluctuations of the neutron source on its capability for void fraction measurement was examined and a counting strategy was recommended to reduce the resulting bias.</p> <p>From the steady-state measurements of the radial void profiles and the gas and liquid flowrates, estimates of important flow parameters were obtained for the fully-developed bubbly and annular flow regimes. These estimates indicated that the flow parameters remain essentially constant for a specific flow regime.</p> <p>To reduce the experimental effort considerably, an alternative method was presented which enables the designer to evaluate these parameters by performing a single experiment where the radial void profile is measured. Based on the momentum equation and Prandtl's turbulent mixing length hypothesis, a general form of the shear stress radical distribution was derived and intergrated to yield the radial profile of the mixture velocity. By combining the radial profiles of the mixture velocity and void fraction, the values of the flow parameters were predicted. The proposed method indicated systematic variations of the flow parameters with the gas and liquid flowrates which were not consistent with observations. The estimated flow parameters, however, were shown to be adequate to predict the average void fraction without introducing appreciable errors.</p> <p>The results of the current experimental observations and analysis were compared with selected models and correlations which have been used by many designers to describe two-phase flow behaviour. This was due to evaluate the validity of the assumptions made in deriving these models and correlations. In general, this comparison indicated that the present experimental results and model predictions were consistent with expectations and previous observations and predictions. However, many of the published models and correlations were found to yield misleading results and conclusions which were attributed to the simplifying assumptions included in their derivation.</p> <p>The void propagation equation was applied to predict the transient response of void fraction to perturbations in the gas flowrate in the adiabatic gas-liquid flow system employed. To solve this equation, values of the distribution parameter are required under changing flow conditions. It is usually assumed that the parameter values obtained for steady-state, fully-developed flow are valid under transient developing-slow situations. That is to say that the steady-state distribution parameter pertaining to the local average voidage condition applies in the transient system. Since this parameter cannot be obtained from steady-state experiments under all voidage conditions experienced during the transient, a continuous functional relationship was assumed in order to interpolate over those regions where the parameter cannot be obtained.</p> <p>An analysis was performed to examine the sensitivity of the predicted void transient response to errors in the distribution parameter. This analysis showed that a comparison between predicted and observed void transient responses should permit the evaluation of the validity of the assumptions made concerning the distribution parameter and its interpolating relationship. A satisfactory agreement between these responses was obtained in bubbly flow. This indicated that the steady-state values of the distribution parameter for fully-developed flow and the assumed interpolating relationship can be used to predict the void transient response in the considered experimental apparatus over the flow conditions studied herein.</p> / Doctor of Philosophy (PhD)

<p>Although adsorption of organic contaminants from the aqueous phase onto activated carbon is a widely used process, mechanistic models capable of describing the performance of adsorption beds are not presently available. Such models, if available, would allow an improved understanding of the behaviour of adsorption beds and could reduce the number of pilot plant studies which are presently required for system design. To develop a mechanistic model of activated carbon adsorption a two part study was undertaken.</p> <p>In the first part, existing adsorption kinetic models were investigated and were found to be incapable of describing the adsorptive behaviour. Based on the structural properties of activated carbon, a branched pore kinetic model is presented which separates the carbon particle into two regions, a rapidly diffusing region which is associated with pores which are significantly larger than the adsorbing molecules, and a slowly diffusing region which is associated with pores which are of a comparable size to the diffusing molecules and in which diffusion is retarded. Equilibrium and batch kinetic experiments were conducted with pure phenolic compounds as adsorbates, and the model parameters were calculated from the data. The analysis shows that the slow diffusion region is important, and that some previously inconsistent results reported in the literature, such as premature breakthrough and tailing of the breakthrough curves, are due to the neglect of this factor. When used in a model of an adsorption column, the kinetic parameters calculated from the batch experiments enabled the performance of experimental adsorption columns to be predicted with excellent accuracy over extended periods. The early breakthrough and characteristics tailing noted above are shown to be a result of uptake in the slow diffusion region. The model as developed originally assumed a surface diffusion mechanism was responsible for transport in the rapidly diffusing region and as a result, solution of the model required extensive computation. The use of the quadratic driving force assumption was investigated to replace the surface diffusion mechanism and its use is shown to significantly reduce the solution complexity while giving an equally good interpretation of the data.</p> <p>In the second part of the study the adsorptive behaviour of two feedstreams of environmental importance was studied. As in the first part, equilibrium and batch kinetic experiments were conducted and parameters for the quadratic driving force branched pore model were obtained by comparing the model to the data. Adsorption column experiments were conducted over extended periods and when the batch determined parameters are included in the adsorption bed model, the bulk of the breakthrough curve is shown to be well predicted. Because of the complexity of the feedstreams treated, the concentration can only be quantified in terms of a non-specific parameter such as Total Organic Carbon (TOC) and all the kinetic constants must be evaluated in terms of this parameter.</p> <p>As with the pure solutes in the first part of the study, the slow diffusion region is very important in the absorptive uptake of these complex organic contaminants. Removal by biological mechanisms is often suggested when adsorption columns continue to exhibit an uptake capacity after prolonged periods of operation, and the problems in differentiating between very slow adsorptive uptake and biological removal are discussed in detail. The present analysis shows that in many cases this removal may be due to continued slow adsorption rather than biological oxidation of the organics. The slow diffusion also has important consequences for the design of activated carbon contactors as contact times far in excess of current practice are indicated if maximum use is to be made of the adsorptive capacity.</p> / Doctor of Philosophy (PhD)

<p>In continuous emulsion polymerization that commercially important phenomena of sustained oscillations and large start-up transient conversion overshoots have been observed by several investigators. Experimental studies have shown that the conversion, number of polymer particles and all other related properties often oscillate with time. In other words a steady state is never achieved. These oscillations can lead to emulsifier levels too small to adequately cover polymer particles with the result that excessive agglomeration and reactor fouling can occur. Furthermore, excursions to high polymer concentrations, due to the cycling behavior of conversion can result in excessive branching and poor polymer processability. It is evident that this reactor behaviour is highly undesirable since it results in a continuously varying product quality.</p> <p>In this thesis, the complex physical and chemical phenomena occurring in a continuous emulsion polymerization reactor are studied both experimentally and mathematically. Dynamic models suitable for prediction and on-line control studies are developed based on particle age distribution. On-line techniques are developed to measure some states of the control model and to monitor the reactor performance. These techniques are based on turbidity measurements and liquid exclusion chromatography. A multivariable stochastic control algorithm is developed to control the pathological behaviour of continuous emulsion polymerization reactors and ensure a high productivity and product quality.</p> / Doctor of Philosophy (PhD)

<p>This dissertation is a theorefical investigation of simultaneous free and forced convection for flow around a sphere or cylinder. This involved a numerical solution of the Navier-Stokes and energy equations by finite difference methods. To this end faster computational techniques were developed. A large number of solutions were computed permitting a significant extension of fluid-mechanical data available in the literature.</p> / Doctor of Philosophy (PhD)