<p>In the first part of the thesis, control of the full molecular weight distribution (MWD) in a semi-batch polymerization reactor is considered. A new batch-to-batch optimization methodology for producing a desired MWD using an approximate fundamental model is presented. The optimization approach is also extended for use as an on-line control method by incorporating a multivariable statistical process control (MSPC) monitoring scheme. The combined MSPC/batch-to-batch optimizer is demonstrated on a simulated semi-batch polystyrene reactor and is shown to be very effective in reacting to large process upsets. Despite significant process/model mismatch, the batch-to-batch optimizer is able to adjust the process and produce the desired MWD within several batches following a process upset. In the remainder of the thesis, dimensionality issues in product quality control are addressed. First, indirect control of the full MWD by directly controlling only the average of the distribution is illustrated. It is shown that the choice of manipulated variables has an important impact on the controller performance when the full MWD is considered, and controlling a single average chain length sometimes causes the MWD to degrade. A simple analysis tool, called the Disturbance Inflation Factor (DIF), is introduced to evaluate which controlled and manipulated variables result in the best overall control of the full MWD. It is shown that with prudent choices of manipulated and controlled variables, simple single variable control can provide significant improvements in the full MWD. Controlling new linear combinations of the original inputs and outputs is also shown to be a feasible option for minimizing the overall effect of the disturbances. Finally, the thesis concludes with a critical review and unification of existing methods for Reduced Dimension Control. It was found that due to the different industries from which the applications originate, there is little or no comparison of similar approaches, thus there is the need for a unification. (Abstract shortened by UMI.)</p> / Doctor of Philosophy (PhD)

<p>High molecular weight poly(ethylene oxide) (PEO) is used in conjunction with a cofactor such as phenol formaldehyde resin (PFR) as flocculants for newsprint manufacture. The objectives of the work described in this thesis were to prepare flocculants superior to PEO and to determine the flocculation mechanism. A series of novel comb copolymers consisting of a polyacrylamide backbone with short pendant poly(ethylene glycol) (PEG) chains was prepared and characterized. Additionally, polymerization conversion curves and reactivity ratios were measured. An interesting finding was that the reactivity of the macromonomer in free radical copolymerization decreased with PEG chain length.</p> <p>Flocculation results with both model latex dispersions and commercial wood pulp suspensions showed that copolymer chain length was the most important variable; molecular weights greater than 3 million were required for good flocculation. On the other hand, the PEG pendant chains could be as short as 9 ether repeat units. Also, only 1 to 2 PEG chains for every 100 acrylamide backbone moieties were required.</p> <p>No published flocculation mechanisms could predict all the behaviors of the PEO or copolymer system. A new mechanism called complex bridging was proposed. According to this mechanism PEO or copolymer chains aggregate in the presence of cofactor to form colloidally dispersed polymer complex which heteroflocculates with the colloidal particles.</p> <p>Given in this work is the first explanation of the requirement for extremely high PEO or copolymer molecular weights for flocculation. It is proposed that polymer chains with molecular weights less than 10⁶ collapse in the presence of PFR to an inactive precipitate before flocculation can occur whereas complexes based on very high molecular weight PEO collapse slowly enough to permit flocculation.</p> <p>Published mechanistic studies are hindered by the fact that PFR has poorly defined structures. It is shown for the first time in this work that well-defined, linear, poly(p-vinyl phenol) (PVPh) is an effective cofactor.</p> / Doctor of Philosophy (PhD)

<p>An integrated methodology based on Stockmayer's bivariate distribution for the dynamic mathematical modelling of the kinetics of olefin polymerization using heterogeneous and homogeneous Ziegler-Natta catalysts has been developed. This methodology uses polymer characterization via size exclusion chromatography (SEC), temperature rising elution fractionation (TREF), and carbon-13 nuclear magnetic resonance (¹³C NMR) to estimate polymerization kinetics parameters and provide information about the types of active sites of the catalyst.</p> <p>A novel and versatile mathematical model for the dynamic simulation of binary copolymerization of olefins using Ziegler-Natta catalysts has been proposed. This model calculates the complete distributions of chemical composition and molecular weight of polyolefins made with catalysts containing multiple active site types and subject to intraparticle mass and heat transfer resistances. This model has a very attractive mathematical formulation that permits easy adaptation to situations in which intraparticle mass and heat transfer resistances are negligible and can also be conveniently combined with mathematical models for the dynamic macroscopic simulation of polymerization reactors for process simulation, optimization and control studies.</p> <p>The homopolymerization of propylene and ethylene using a titanium-based heterogeneous catalyst was investigated. The presence of hydrogen during the polymerization of propylene was found to increase the rate of propylene polymerization by creating new active site types. This was clearly shown using SEC and TREF analyses of the polypropylenes.</p> <p>A systematic methodology for the deconvolution of the molecular weight distribution (MWD) of linear polyolefins made with multiple site type catalysts has been developed. The MWD of polyolefins measured by SEC is deconvoluted into individual most probable chain length distributions using a mathematical method that takes advantage of the conditional linearity of the optimization problem.</p> <p>A mathematical model for simulation of TREF fractionation of binary copolymers made with multiple site type catalysts using Stoclanayer's bivariate distribution has been developed. This is the first time a mathematical model is proposed to describe the MWD of TREF fractions using a phenomenological approach considering the influence of the bivariate distribution of molecular weights and copolymer composition in the fractionation. The modelling of TREF with this model provides an ideal limiting case for the fractionation of binary linear copolymers with broad molecular weight and composition distributions and is useful in interpreting TREF fractionation results.</p> / Doctor of Philosophy (PhD)

<p>A dynamic simulation of the pilot scale fluidized bed reactor in the Department of Chemical Engineering is developed based on mass/energy balance equations of the process. The unknown parameters in the model equations are estimated using dynamic data from the reactor. A preliminary control strategy for the reactor system is tested by simulation, and the results are used to aid in the implementation of the control system to the reactor. The control strategy is a cascade control system in which the inner loop regulates reaction temperature by proportional-integral control, using the ratio of hydrogen to n-butane feedrates as manipulated variable. The outer loop is a Dahlin's algorithm controller. which maintains the selectivity of propane at a specified setpoint by manipulating the reaction temperature setpoint to the inner loop.</p> <p>The control system performed less favourably on the real system than it did on the simulation model. This result is attributed primarily to the inability of fixed-parameter controllers to deal with highly non-linear and time varying processes. Alternate control methods are suggested which are designed to deal with these problems.</p> / Master of Engineering (ME)

<p>The effect of polystyrene beads and nylon fibres on the permeability of bleached kraft pulp fibre beds was studied experimentally. Three types of experiments: 1) constant head filtration, 2) elastic permeation, and 3) fixed bed permeation were carried out. Four types of fibre beds were used: 1) pulp fibres only, 2) pulp fibres and plastic beads, 3) pulp fibres and nylon fibres, and 4) pulp fibres, nylon fibres and plastic beads. The beads used were 80 μm in diameter while the diameter and the length of the nylon fibre were 45 μm and 1.89 mm respectively. The beads were used as a model for dispersed air bubbles in pulp suspensions, while the nylon fibres were chosen because their specific surface area and specific swollen volume were close to those of the beads.</p> <p>In a filtration experiment, a fibre bed was formed from the corresponding suspension while pressure drop across the bed and cumulative filtrate weight were recorded: Specific filtration resistance values for the suspensions were calculated from the filtrate weight data. It was observed that specific filtration resistance increased with bead content in the slurry while filtration resistance decreased with an increase in the content of nylon fibres in the suspension. A mathematical model based on permeation equations was derived to simulate the filtration process.</p> <p>In a permeation experiment, the fibre bed formed in a filtration experiment was subjected to a complete recovery-compression cycle starting with the maximum pressure drop. Flowrate of water through the bed and the thickness of the bed were measured as a function of the pressure drop. Fibre beds of the four different compositions all displayed hysteresis in both the flowrate and bed thickness data. Bed thickness data were correlated by regression analysis and under flow induced compression the thicknesses were found to be linear or nearly linear functions of the pressure drop acting across the bed. The presence of plastic beads did not affect the structure and thickness of the beds, suggesting that the plastic beads were able to fit into the pores of the pulp bed without disrupting the structure. By contrast, nylon fibres increased both the permeability and the thickness of the bed because of the formation of a more open network structure. The mathematical model proposed by Jonsson and Jonsson was used to predict compression behaviour; however, the concave form of plot of thickness versus pressure drop during recovery was not predicted by any of the current bed compressibility models.</p> <p>Permeability of the compressed bed formed in the filtration experiment was measured in a fixed bed permeation experiment. Permeability of the bed was used to calculate the specific external surface area and specific swollen volume of the bed materials using the Kozeny-Carman equation. It was found that for both the pulp/bead system and the pulp/nylon fibre system, the specific surface area and specific swollen volume of the bed were linear functions of the content of polystyrene beads or nylon fibres. The specific surface area and specific swollen volume of beds that contained pulp fibres, nylon fibres and plastic beads were predicted, within 7%, by the linear supposition of the specific surface area and specific swollen volume of the bed constituents. This analysis is important because it permits estimation of the effect of air bubbles on the permeability of pulp pads in various processes in the pulp and paper industry.</p> / Doctor of Philosophy (PhD)

<p>3-D numerical analysis of a viscoelastic flow is a necessity for better understanding of viscoelastic fluids and viscoelastic flow. It is important both from the scientific and technological points of view. Analysis of viscoelastic flow is a difficult task as it is associated with the problems arising from intrinsic complexity of the fluid. Progress in the area of 3-D analysis of viscoelastic flow has been further hindered by the increase in the size of the problem and number of variables. The outlet boundary condition for 3-D flow of a viscoelastic fluid is another problem. Segregated methods were used to solve the creeping flow formulation of the duct flow to save computer time and memory. A pressure correction method was selected and compared with the fully coupled method. A 3-D and 2.5-D segregated algorithm were proposed using the modified Phan-Thien Tanner constitutive equation and the EVSS method to decouple the calculation of stresses from the flow kinematics. Results from the 2.5-D algorithm were verified by comparison with the reported results from literature. Results for cases of high Wi were obtained and it was shown that for MPTT fluid, the intensity of the secondary flows becomes independent of Wi at high Wi. The effects of Re on the secondary flows were also studied and new patterns of secondary flows involving up to eight vortices in each quarter were reported. Results from the 2.5-D analysis were compared with the results of a 3-D algorithm in the analysis of the viscoelastic flow in straight ducts. Different cases of boundary conditions were studied and observations are reported. It is reported for the first time that a deviation from a fully developed solution occurs near the outlet. The problem of the destruction of the vortex pattern and the consequent increase in the primary flow velocity component were then analysed. It was established that the fully developed flow solution is a valid solution for the 3-D formulation of the problem and the problem arises from a combination of the decoupling of the stresses and imposing outlet boundary conditions. The 3-D algorithm was further evaluated for the cases of flow in complex geometries, using two test cases from the literature. One of the cases involved a converging duct and the other involved a 4:1 abrupt contraction. Results from 3-D and 2-D planar analysis were compared with the reported experimental results.</p> / Doctor of Philosophy (PhD)

<p>The effect of capillary dimensions on the extrudate swell of molten polymers is studied with three branched low-density polyethylenes (LOPE) and a broad distribution polystyrene (PS) samples. The polystyrene and one of the low-density polyethylene samples (DHDY-6873) are tested in detail at three extrusion temperatures ranging from 160°C - 220°C, while the other two low-density polyethylene samples are run at one temperature only.</p> <p>For all polymers, extrudate swell decreases exponentially with increasing length-to-diameter (L/D) ration of capillaries. For a die-orifice (L/D → 0), extrudate swell increases with entry angle up to 150° and decreases thereafter. At constant reservoir diameter DR, extrudate swell also increases with DR/D ratio up to 18 and then drops.</p> <p>An empirical decay equation is found to correlate well with the extrudate swell data for low-density polyethylenes. However, there is no direct correlation for polystyrene.</p> <p>Huang and White's new expression predicting extrudate swell with long capillaries does not correlate reasonably well with the experimental data for polystyrene. However, the model as previously suggested by Graessley gives better approximation. Tanner's new inelastic theory on extrudate swell plays no significant part in the present study. The effect of "frozen-in-stresses" on extrudate swell is found to be small.</p> <p>Huang and White's new model predicting extrudate swell for an orifice-die correlates well with the polystyrene data at low shear rate region (<30 1/sec), but indicates considerable discrepancy at high shear rate region. At present, there is no reilable predictive theory for extrudate swell at higher shear rates both with short and long capillary dies.</p> / Master of Engineering (ME)

<p>The efficient design of extraction columns calIs for the accounting of flow non idealities, collectively termed axial mixing, in the phases involved. Axial mixing occurs mainly through back-mixing caused by circulation, wake transport with dispersed drops and induced turbulence due to mechanical agitation. Non uniform velocity profiles and forward mixing due to drops of different sizes are the other factors. A new factor identified to significantly enhance back-mixing, is the increase in the density of the continuous phase with column height termed as the unstable density gradient. In this thesis, attention was focussed on this factor using a 5 cm reciprocating plate extraction column (RPC). A new approach based on the Kohnogoroff isotropic turbulence theory was developed to model the continuous phase back-mixing under two phase flow conditions. The contribution due to mechanical agitation, dispersed phase flow and the unstable density gradient were accounted in the model in terms of their respective energy dissipation rates and mixing lengths. The parameters were estimated by fitting the model to the experimental data obtained through the steady state tracer injection technique under non mass transfer conditions. The results showed that the unstable density gradient played an important role in enhancing the back-mixing even though its energy dissipation rate was very small relative to the other two contributing factors. This was due to the large mixing length associated with the unstable density gradient effect. At high mechanical agitations, the contributions of the dispersed phase and the density gradient declined. A preliminary study was also performed to investigate the unstable density gradient effect under mass transfer condition. Water was used as the solvent to extract i-propanol from lsopar M drops in the extractor. As increasing amount of alcohol was extracted, the density of water decreased leading to an unstable density gradient. To ensure the reliability of the estimation of the back-mixing coefficient (Ec), a non transferring tracer dye was also injected steadily into the continuous phase. Ec values were determined simultaneously from the concentration profiles of the tracer and the solute, thereby providing two independent estimates for each experiment. The results were comparable under most operating conditions thereby validating the tracer technique. The dispersed phase hold-up, drop size and the mass transfer coefficient were also estimated and compared critically with the models available in literature. The hydrodynamics in the column were significantly altered by the interfacial effects associated with the transfer of solute from the dispersed phase to the continuous phase. In particular coalescence was promoted leading to large drops. Under these conditions the Kolmogoroff model could not isolate the influence of the density gradient from other contributing factors. However the experimental results clearly showed an enhancement in the back-mixing relative to the non mass transfer case. Based on these observations it is concluded that care must be taken to avoid the unstable density gradient created either inadvertently during tracer measurements involving ionic compounds or during mass transfer.</p> / Doctor of Philosophy (PhD)

<p>The creation of a homogeneous polymer melt from powder particles, which involves particle coalescence followed by the formation and dissolution of bubbles, is a situation encountered in processes such as rotational molding and powder coating. The present work focuses on the study of the transformation of a loosely packed, low density powder compact, to a fully densified polymer part, when processed at temperatures above the melting (or glass transition) point of the polymer. The purpose of this work is to study the appearance of air pockets, or bubbles, which are trapped during the melting-sintering of the polymer particles, to elucidate the mechanisms involved in their formation and subsequent dissolution and to propose models which are suitable for the description of the overall densification of the powder compact. A comparative study of the processing characteristics and properties offered by various polymers has been undertaken. During this work, the problem of the presence of excessive bubbles has been encountered mainly in polymers with high amorphous contents and low crystallinities. Rheological characterization suggested that these types of polymers typically exhibit weak viscosity dependence on temperature and higher melt elasticities. The formation of bubbles and their subsequent dissolution have been studied experimentally. Various types of polymers have been examined, in an effort to identify the important material parameters affecting bubble formation and to elucidate the mechanisms involved. The evolution of density as a function of time during sinter-melting was measured experimentally, using a heating oven. The results revealed that the overall process consists of two stages: Particle coalescence, which depends on viscosity, surface tension and powder properties, occurs during the first stage, during which air pockets, which eventually become bubbles, are entrapped inside the melt. The second stage involves the shrinkage and eventual disappearance of the bubbles. The experimental results were compared to models commonly used in the ceramics, glass and metals processing literature for the densification of particulate compacts. Application of models based solely on viscosity and surface tension phenomena, can describe satisfactorily the process until the point where closed pores (bubbles) form. The latter stage of bubble dissolution has been addressed by modeling the dissolution of a single spherical bubble in an infinite polymer melt under isothermal conditions. The bubble dissolution model has been successfully applied to provide predictions of density as a function of time for the late stages of densification.</p> / Doctor of Philosophy (PhD)

<p>A new kinetic theory for free radical copolymerization with long chain branching and crosslinking is proposed. This kinetic theory accounts for the history of the generated network structure as well as for all of the important elementary reactions in free radical polymerization. The present theory can be used to make calculations of various important properties such as onset of gelation, weight fraction of sol and gel, number- and weight-average chain length of sol fractions, crosslinking density in sol and gel fractions, etc. Since free radical polymerization is kinetically controlled, each primary polymer molecule experiences a different history of crosslinking and cyclization. The present theory proves the existence and permits the calculation of the crosslinking density distribution, although all statistical models which assume an equilibrium system inevitably employ the assumption that the crosslinking density is the same for all chains. The existence of a crosslinking density distribution with a significant variance is an important feature of the present kinetic theory stating that polymer networks synthesized by free radical polymerization are inherently inhomogeneous on a microscopic scale. This theory reduces to the Flory/Stockmayer theory under Flory's simplifying assumptions and may therefore be considered a general mean-field theory.</p> <p>The present theory was successfully applied to the copolymerization of methyl methacrylate/ethylene glycol dimethacrylate, and acrylamide/N,N'-methylene-bis-acrylamide. In real systems it was found that the effect of cyclization (intramolecular reactions) and the decreased reactivity of pendant double bonds relative to the monomeric double bonds are important.</p> <p>This new kinetic theory should assist one to design superior quality network polymer systems and it can also be used to control various polymerization processes. It was found that if branches are formed by chain transfer to polymer the crosslinking density is always higher in continuous stirred tank reactors (CSTR) than in batch reactors, however, this is not true in general for vinyl/divinyl copolymerizations. The variance of the crosslinking density distribution in CSTR's is large due to their broad residence time distributions.</p> / Doctor of Philosophy (PhD)