<p>"DYNSYS" is a digital simulation package for modelling the dynamic behaviour and automatic control of complex industrial systems. An acronym for Dynamic Systems Simulator, it was developed in the late 1960s in the chemical engineering department at McMaster University, The underlying principle of "DYNSYS" is that of modularity; i.e., the user assembles mathematical models of process units and control devices to build the process whose transient behaviour is to be studied. A fundamental aspect of dynamic simulation is the numerical solution of ordinary differential equations (o.d.e.s). The original version of "DYNSYS" used a third order Adams-Moulton-Shell routine; however, this is not sufficient to handle stiff systems, i.e., systems where the time constants differ greatly in magnitude. In chemical engineering, stiff o.d.e.s occur widely in reaction kinetics and to some extent in multistage systems.</p> <p>Conventional numerical techniques are restricted by stability to using a very small step size resulting in large computer times. There have been many new numerical techniques published in the recent literature directed at the efficient numerical solution of systems of stiff o.d.e.s. A literature survey of these has been made.</p> <p>Numerical testing of several methods indicated Gear's method to be superior. It is a variable order, variable step, linear, multistep method.</p> <p>Most stiff techniques are implicit and require a technique such as Newton-Raphson iteration to converge. Each iteration involves the solution of a system of linear algebraic equations (usually sparse) equal in size to the number of o.d.e.s. For a large stiff system, this requires considerable computer time. Various sparse linear equation solvers have been evaluated and that a Bending and Hutchinson appears to be the most efficient. Their routine stores and operates on only the nonzero elements of the equations. When the equations are solved for the first time, a string of integers called the "operator list" is created which stores the particular solution process by Gaussian elimination. If the system is re-solved using the operator list, the amount of computer time required is greatly diminished. If the zero elements remain zero and the nonzero elements change, the same "operator list" can be used to solve the new system. This is essentially what occurs during the numerical integration. The operator list could be set up on the first integration step and used on later steps to solve each new linear system.</p> <p>Gear's integration algorithm in conjunction with the Bending-Hutchinson linear equation solve has been implemented into DYNSYS version 2.0. An option for stiff systems with tridiagonal Jacobian matrix is also included. The procedure for writing module is outlined.</p> <p>Four small examples are presented to illustrate the new executive:</p> <p>(1) The level control of a stirred tank system (nonstiff) with time delay.</p> <p>(2) A network of 15 stirred tank reactors, stiff and nonstiff, 2 o.d.e.s per reactor.</p> <p>(3) A tubular reactor with 222 stiff o.d.e.s. resulting from the discretization of the partial differential equations.</p> <p>(4) A tubular reactor with 49 stiff o.d.e.s with tridiagonal Jacobian matrix.</p> <p>A simulation of a fictitious chemical plant proposed by Williams and Otto is also described.</p> / Doctor of Philosophy (PhD)

<p>This thesis contains four studies of transport phenomena and blood platelets.</p> <p>The initial stage in thrombus formation is platelet adhesion to a foreign surface: platelets diffuse to the surface and then bind to it. Experiments were performed to examine the influence of haematocrit, platelet concentration, shear rate and drugs upon platelet diffusivity, the platelet wall binding rate constant and the saturation level of platelet adhesion to the surface. The level of platelet adhesion to collagen coated glass tubes were determined by measuring the axial distribution of 51Cr-γ-ray emissions from adherent 51Cr labelled platelets. The results demonstrate that the model of Grabowski et al (1972) adequately describes platelet adhesion to foreign surfaces, that platelet adhesion obeys intermediate kinetics, that the plasma skimming layer can be ignored and that platelet diffusivity is enhanced by the complex motion of red cells. An explanation for contradictions in the literature regarding the effect of drugs upon adhesion is suggested.</p> <p>A design for data collection and analysis was devised for experiments in which the distribution of tracer in multicompartment systems is followed. The design requires the provision of multiple responses and analysis with a Bayesian multivariate technique. It deals with the problems of lumping and ill-conditioning inherent in descriptions of tracer distributions. The design proved successful in characterising the exchange of serotonin between the granules and cytoplasm of rabbit platelets and their surrounding medium in in vitro experiments using washed rabbit platelets.</p> <p>In vitro, serotonin is freely exchangeable between platelets and their surrounding medium. To describe the potential behaviour of platelet serotonin in vivo, models were devised and fitted to the data resulting from dual label, 51Cr and 14C-serotonin, survival curves. The simplest model that adequately described the data was one in which serotonin was assumed to exchange at a finite rate between circulating platelets. The exchange rate constant from platelet to surrounding was similar to that determined in vitro.</p> <p>The behaviour of adenine nucleotides in vitro and in vivo have been investigated experimentally (Reimers et al, 1975b). The in vitro exchange of adenine nucleotides between a metabolic pool and a granule pool is adequately described by first order kinetics. This information was used in a model that was fitted to data from adenine nucleotide survival and release studies. No significant metabolism or release of platelet adenine nucleotides was found in vivo.</p> / Doctor of Philosophy (PhD)

<p>This study examined at pilot scale the application of dynamic control with a step feed activated sludge process for control of effluent quality. Computer simulation and pilot studies were used to develop a process control strategy involving the Specific Oxygen Utilization Rate (SCOUR). This control was applied using a real-time minicomputer system. Comparisons were made to a single compartment completely-mixed process operated in parallel to the controlled system.</p> <p>The control strategy attempted to maintain SCOUR at a desired setpoint in the final compartment of a three reactor step feed system. Optimal influent contacting patterns were continuously calculated for the first and third compartments to satisfy the control objective. Unique optimization was not possible if the flow distribution was made to three compartments.</p> <p>Using a SCOUR setpoint of 15 mgO₂/g MLSS-h filterable organic carbon effluent data suggested that a reduced effluent variability can be obtained during high loading periods. At low loadings when SCOUR control was limited, no improvement of effluent TOC was obtained.</p> <p>With SCOUR control, consistently higher effluent solids concentrations were observed. High effluent suspended solids concentrations for the controlled system were probably caused by the inefficient oxygen transfer by the diffuser aeration system in the pilot plant.</p> / Master of Engineering (ME)

<p>This thesis is a study of the effect of surfactant on the film thinning behaviour of small, single droplets coalescing at a planar interface in oil/water systems. There are two major parts in this thesis. The first is the mathematical modelling of film thinning, and the second is the experimental measurement of the variation of film thickness during thinning.</p> <p>The mathematical modelling consists of:</p> <p>(i) the development of a film thinning model in which the interface mobility is calculated and not assumed arbitrarily,</p> <p>(ii) the numberical solution of this film thinning model based on a polynomial representation of the pressure in the film,</p> <p>(iii) the extension of the parallel disc model to describe the thinning at the barrier ring for uneven thinning, by allowing the interfaces to have varying degrees of partial mobility, and</p> <p>(iv) the algebraic analysis of a postulate for the conditions for even and uneven thinning, based on the assumption that the pressure in the film is a parabolic function of the radial distance. To verify these models, their predictions are compared with experimental observations.</p> <p>In the experimental part, the effect of additions of palmitic acid and the effect of drop size and bulk interface age on the film thinning behaviour of toluene drops have been investigated using the white light interference technique. A novel drop forming technique has been developed, by which one drop forming nozzle can be used to form drops of different sizes without piercing the bulk interface; this technique eliminates the possibility of surfactant transfer between the bulk and drop interfaces.</p> <p>New observations of film thinning behaviour are reported. These are the uneven thinning pattern that occurs when both the drop and bulk interfaces have the same surface concentration, and new thinning patterns which occur when drops are released to the bulk interface in rapid succession.</p> / Doctor of Philosophy (PhD)

<p>A pilot plant fluidized bed reactor in which complex and highly exothermic catalytic hydrogenolysis reactions are taking place, is being used to investigate the computer control of temperature, conversion and selectivities in such reactors. The process is highly nonlinear, characterized by asymmetric dynamics and considerable change in catalyst activity. Moreover, a deadtime of 360 s is introduced by an on-line process gas chromatograph employed to obtain the composition measurements. As a result, the cascade control system comprising a proportional-integral controller for reaction temperature in the inner loop and a Dahlin controller for propane selectivity in the outer loop was reported in previous works to have performed well in certain regions of operation at a given time but revealed very oscillatory and nearly unstable performance in other regions or at different times.</p> <p>This nonlinear behaviour of the reactor is further investigated. It is found that by better matching the process response characteristics and by detuning the Dahlin controller, this unstable oscillatory behaviour of the cascade control system can be overcome and acceptable performance can be achieved over a wider range of operating conditions. Later, self-tuning adaptive controllers are tried in an attempt to better account for the changing gains and time constants of the nonlinear process, as well as for the time-varying catalyst activity. The cascade control scheme with Dahlin and Self-tuning regulator (STR) demonstrated excellent performance. Finally a double STR configuration for both the inner and outer loops in carried out. Problems associated with this implementation are discussed and possible improvements suggested.</p> / Master of Engineering (ME)

<p>Various models of the nuclear reactor system are developed and evaluated in order to provide insight on the fundamental phenomena involved in the coolant void effect as a guide to future simulation studies and experimental design.</p> <p>The mathematical description of the fundamental phenomena and consideration of the macroscopic physical characteristics define models for the neutron flux density and the coolant void fraction for the case of boiling-light-water nuclear reactors. Experimental comparisons are made whenever possible to evaluate the effectiveness of those models. The two-group neutron diffusion model and Hancox's void model were found necessary to describe the steady state behaviour of the nuclear reactor cell. The errors and limitations of present day models and techniques are delineated; the directions for improvement are also indicated. In general, it was found that independent experimental estimates of the fundamental parameters are needed to replace the current reliance on extensive experimental model correlations. In this way the need for expensive prototypes can be eliminated.</p> <p>A temporal transformation of the general space-time neutron equations is developed to facilitate their solution by standard numerical techniques. It was found that the computation time can be reduced over threefold for transient control problems.</p> <p>The coupling of the fluid model and the neutron flux model proves most interesting and shows that coolant voiding can have a profound effect on both the steady state and the transient behaviour of nuclear reactors. It is also shown that errors in present day techniques for investigating the coupling effect can lead to errors in reactivity estimates of more than the prompt critical limitation.</p> / Doctor of Philosophy (PhD)

<p>A general kinetic model which accounts for diffusion-controlled termination and propagation in free-radical copolymerization up to high conversions was developed. This model was tested on batch kinetic data for styrene/p-methyl styrene thermal copolymerization and data on the chemically-initiated bulk copolymerization of methyl methacrylate/p-methyl styrene. The model gave reasonable predictions of conversion, copolymer composition and molecular weights for these copolymer systems and thus should find use in the design, optimization and control of copolymer reactors.</p> / Doctor of Philosophy (PhD)

<p>Canada and the United States by the "Great Lakes Water Quality Agreement" have designated that the discharge of phosphates in sewage to the Great Lakes will be controlled. In the majority of cases, chemical precipitation is the treatment method to be used. The selection of the chemical dosage needed is empirical and requires that extensive experimental studies be carried out at each wastewater plant.</p> <p>The problem of estimating the chemical dosage is approached in this work on a more fundamental basis. The precipitation of phosphates with lanthanum is assumed to be representative of a chemical system at a metastable equilibrium. The dosage which results in the desired aqueous phosphate concentration at this state is estimated with an equilibrium model of the system. This model includes the reactions of major inorganic species found in wastewater.</p> <p>Lanthanum is an efficient precipitating agent which causes a low residual phosphate concentration to result, even when added in quantities based upon the stoichiometric requirements. Also, lanthanum can be recovered by an economically viable process and recycled.</p> <p>The solubility products of lanthanum, ortho-, pyro- and tripolyphosphate, lanthum hydroxide and carbonate and the stability constants of the hydroxide and polyphosphate ion complexes were measured. The experiments were carried out in distilled water at ion concentrations typical of the magnitude to be used in an actual treatment process. With this information, and solving the complex chemical equilibria problem for a set of over fifty separate reactions, it is shown that the extent of precipitation of ortho- and polyphosphates from a municipal wastewater can be accurately predicted. A computer program was written to predict the lanthanum dosage required for a specific residual of dissolved phosphates given the water quality of the wastewater expressed as the total aqueous concentrations of ortho- and polyphosphates, calcium, magnesium, carbonates, sodium, chloride, sulphates and pH.</p> / Doctor of Philosophy (PhD)

<p>Robert Frank Moore: A Computer Aided Design Package for Time Series Analysis. M.Eng. Thesis, McMaster University, Hamilton Ontario, February 1982.</p> <p>Control problems often require a reasonable and adequate model for forecasting or control. An interactive computer package is presented which allows the iterative determination of a stochastic and transfer function model for single input/single output experimental data. Note that time series analysis techniques present various quantitative measures of model adequacy for this type of model. User familiarity with time series analysis is essential in the determination of a reasonable, parsimonious model during an interactive session with this package.</p> <p>The interactive program provides initial diagnostic tests for the data to aid the estimation of parameters for a user selected model form. The Marquardt non-linear least squares procedure is available to improve the initial parameter estimates. Information for diagnostic testing of the model residuals is then displayed. The option for iteration back to the point of model form selection is available.</p> <p>A multivariable analysis problem may be resolved in a stepwise manner using a non-iterative version of the time series package. This version fits a user selected model to the data and provides diagnostics on the model residuals. The computer package is presently functional on a VAX 11/750 computer. All graphical display characteristics are suitable for a Tektronics 4025 terminal. Programming for the package is in FORTRAN77.</p> / Master of Engineering (ME)

<p>High molecular weight poly(ethylene oxide) (PEO) is an effective flocculant in the papermaking process. The performance of PEO can be greatly enhanced in the presence of second polymeric component. This second component is called cofactor in paper technology literature. In this thesis, poly(vinyl phenol-co-styrene sulfonate (PKS) is chosen as a model cofactor. The mechanism for complex formation between PEO and PKS, the transport properties of PEO/PKS complexes, the relationship between PEO/PKS complex formation and flocculation are discussed. PEO mainly interacts with aromatic groups of PKS through hydrogen bonding and hydrophobic interactions. The widely proposed hydrogen bonding mechanism between phenolic hydroxyl group and ether oxygen is investigated by comparing the complex formation, flocculation performance between PEO/PKS and PEO/poly(styrene-co-styrene sulfonate). Phenolic content, salt, temperature and PEO molecular weight affect the complex formation and flocculation efficiency. A hydrophilic, sterically stabilized and negatively charged colloidal model, dextran sulfate modified precipitated calcium carbonate, is developed to mimic the solution properties of fillers in papermaking flocculation. This work gives a better understanding about PEO/cofactor flocculation mechanism.</p> / Doctor of Philosophy (PhD)