bluuebunny/crossref_metadata_2025_split huggingface dataset:
The optimal control of polymerisation reactors
Authors: Hicks James , Mohan Amar , Ray W. Harmon 
Published: March 2009

AbstractTwo separate but related problems are treated in this paper: (i) the optimal control policy for continuous stirred tank polymerization reactors; (ii) the optimal control program for batch polymerization reactors. The first problem concerns determining the temperature and initiator control policy which brings the reactor to the desired steady state while minimizing some objective functional (e.g. start‐up time, cost of control action, etc.). The second problem is concerned with finding the best temperature and initiator program so that the product from the batch reactor has the best possible molecular weight distribution.Both free radical polymerization and linear condensation polymerization examples are considered with molecular weight distribution moments being used to characterize the polymer. Kinetic parameters typical of styrene are used for the free radical case, and realistic parameters are chosen for the condensation examples. The techniques used can be immediately carried over to other polymerization systems, and hopefully generalizations about the character of the optimal policies for such new systems can be made by considering the policies found for the systems studied. The results of the study demonstrate some of the potential gains possible through supervisory computer control of polymerization reactors.
Vérification expérimentale de l'épaisseur du film pour des liquides non‐newtoniens s'écoulant par gravité sur un plan incliné
Authors: Therien Normand , Coupal Bernard , Corneille Jean L. 
Published: March 2009

AbstractLeg épaisseurs des films liquides de douze solutions polymériques s'écoulant par gravité en régime laminaire, stable, sur un plan incliné ont été mesurées en fonction de plusieurs débits volumétriques du fluide.La valeur théorique de l'épaisseur du film a été calculée en utilisant le modèle rhéologique d'Oswald‐de Waele et en supposant aucun glissement apparent à la paroi.L'étude des résultats obtenus en comparant les valeurs expérimentales et théoriques de l'épaisseur du film porte sur plus de 250 essais et montre en définitive que le modèle d'Oswald‐de Waele permet de prédire l'épaisseur du film liquide avec une erreur relative moyenne inférieure à 4.0%. Cependant des calculs de l'épaisseur du film basés sur un comportement newtonient avec viscosité évaluée à la paroi démontrent clairement que l'épaisseur est peu influencée par la variation de la viscosité au travers du film liquide. Ainsi l'écoulement par gravité sur un plan incliné ne permet pas une vérification rigoureuse du comportement rhéologique des fluides non‐Newtoniens.
An experimental investigation of the influence of the grain size of the metal surface on pool boiling heat transfer
Authors: Nagarajan R. , Adelman Maurice 
Published: March 2009

AbstractThe influence of the grain size of metallic surfaces on nucleate boiling was investigated experimentally. Surfaces of electrodeposited copper, nickel, brass and chromium were studied with particular emphasis on copper (146 grains per inch to 1678 grains per inch). The pool boiling heat transfer studies were conducted by transferring heat produced electrically through a 6‐in. diameter heating surface to a pool of boiling water contained in a glass boiler.A log‐log plot of the Q/A versus δTm data showed a definite effect of the grain size of the surface on nucleate boiling heat transfer, the heat transferred at a given δTm increasing as the grain size increased.For copper plated surfaces, the Rohsenow Equation for nucleate pool boiling gave values for Cst and r, which showed a linear relationship when plotted separately against the number of grains per unit length of the surface. A slightly modified form of the Rohsenow correlation has been proposed which takes into account the influence of the grain size of the surface metal for predicting boiling heat transfer.
A correlation for heat transfer in liquid fluidized beds
Authors: Hamilton William 
Published: March 2009

AbstractA relationship, of the Colburn j‐factor type(9), is derived for heat transfer in fluidized beds. This correlation (10) successfully accounts for the existence of the characteristic maximum heat transfer coefficient at a particular porosity. The derived relationship also predicts the experimentally observed variation of h with change of particle size and density. These variations are mainly a function of the hydrodynamics of the system.
Solubilities of ethane and other gases in normal paraffin solvents
Authors: Hayduk W. , Cheng S. C. 
Published: March 2009

AbstractThe design of a gas solubility apparatus utilizing the basic principle of the Morrison and Billet apparatus is described. The solubilities at atmospheric pressure of ethane in the normal paraffin solvents, hexane, heptane, octane, dodecane and hexadecane, and also of the same gas in the two‐component solvent solutions consisting of hexane and hexadecane are reported. The solubilities of twelve gases were empirically correlated utilizing one constant for each gas. The empirical equations permit an estimate of the solubility in any normal paraffin solvent from hexane to hexadecane and for any temperature between 15°C and 40°C from a single solubility measurement.
Mathematical models for a packed‐bed chemical reactor
Authors: Parisc Jean R. , Stevens William F. 
Published: March 2009

AbstractVarious approaches to the mathematical representation of the simultaneous phenomena of heat transfer, mass transfer, and chemical reaction, within a packed‐bed chemical reactor, are summarized and discussed from the point of view of both accuracy and practicality. After careful analysis of the ideas presented in the recent literature, a relatively simple unidimensional model is proposed for use, both for steady‐state calculations and for dynamic analysis. The assumptions inherent in the use of the proposed model are carefully stated, and areas of uncertainty are pointed out. Reference is made to recent work in which the proposed model has found application.
Identification of parameters in systems of ordinary differential equations using quasilinearization and data perturbation
Authors: Donnelly J. K. , Quon D. 
Published: March 2009

AbstractGiven a set of observed data for a particular physical phenomenon, the problem of computing the “best fit” parameters for the mathematical model describing the phenomenon is a common problem in process or reaction mechanism identification. If the mathematical model comprises a set of non‐linear ordinary differential equations, this leads to a non‐linear boundary value problem. A very powerful way of attacking this class of problem uses an adaptation of the Newton‐Raphson‐Kantorovich procedure, called quasilinearization, which regards the non‐linear problem as the limit of a sequence of linear problems. Starting from an initial trial solution, convergence if it does occur, occurs rapidly; further, convergence is assured if the initial guess is “close enough” to the true solution. The difficulty of making a good initial guess, a serious limitation of the method in the past, can in principle be overcome by the algorithm proposed. When a given vector may not be within the domain of convergence of the original problem, it must be within the domain of convergence of some other derived problem. The latter may then be perturbed towards the original problem in a finite number of steps. In the case of process identification, new data points are derived; these are subsequently adjusted until they coincide with the original data. The algorithm has been successfully applied to several examples from recent chemical engineering literature.
Differential scaling: A method for chemical reactor modelling
Authors: Fuller O. M. 
Published: March 2009

AbstractA mathematical method is presented for the design of partial, distorted models for which specified quantities may be held invariant on change of scale. The method is applied to tabular reactors for homogeneous, gas‐phase reactions and in particular to a prototype reactor designed to produce ketene from acetone. The results for this particular problem are compared with those from modeling methods based on the principle of similarity.
Jet momentum dissipation at a grid of a large gas fluidized bed
Authors: Behie L. A. , Bergougnou M. A. , Baker C. G. J. , Bulani W. 
Published: March 2009

AbstractRational scale‐up of fluidized beds to commercial size requires an understanding of the operation of the grid support plate. One aspect of grid behavior has been studied experimentally; namely, the momentum dissipation of vertical air jets within an 11 inch diameter bed of fluidized cracking catalyst. Nozzle diameters were varied from ¼ to 1½ in. and nozzle velocities from 50 to 300 ft./sec. The data have been found to fit a general correlation relating the normalized axial momentum of the jet to a modified Froude number. The significance of the correlation to the process and design engineer is briefly discussed.
A model fouling reaction in a zeolite catalyst
Authors: Tan C. H. , Fuller O. M. 
Published: March 2009

AbstractA zeolite catalyst became rapidly fouled when used for the alkylation of benzene by cyclohexene at temperatures below 245°C. At higher temperatures, the extent of fouling was limited and at 450° C, a steady rate of formation of cyclohexyl benzene was observed. The fouling material was identified as a mixture of di‐ and tri‐alkyl benzene, trapped because of size in the void spaces of the zeolite crystal.A mathematical model based on the forms of Langmuir‐Hinshelwood kinetics was used to describe the fouling phenomenon. The effect of the internal mass transport has also been investigated by means of a mathematical model. This model indicates that transport between the surface of the zeolite crystal and interior reaction sites is rapidly blocked by a layer of fouling material.
Optimum catalyst formulation for the aromatization of methylcyclopentane
Authors: Jenkins B. G. M. , Thomas W. J. 
Published: March 2009

AbstractThe formation of benzene from methylcyclopentane over platinum impregnated silica‐alumina represents a typical reforming reaction occurring in the presence of a bifunctional catalyst.A detailed experimental investigation enabled a previously established kinetic model of the system to be extended and parameters to be evaluated. By application of the maximum principle the catalyst composition could be formulated so as to maximize the yield of benzene, simultaneously suppressing the formation of undesirable products. For an isothermal reactor operating in a temperature region where chemical reaction is rate controlling, it was found that a constant catalyst composition along the reactor length represents a sub‐optimal policy which, nevertheless, closely approximates the optimal solution. The effect of intraparticle diffusion limitation on the optimum profile is also investigated.The model developed is limited to low conversions for the reaction model under dehydrogenative conditions.
The optimization of reactors with decaying catalyst: The effect of macromixing
Authors: Lee Soo‐Il , Crowe Cameron M. 
Published: March 2009

AbstractThe following general problem is considered: in a catalytic reactor with uniform temperature and a particular residence‐time distribution (RTD), given the kinetics of the reaction and the kinetics of decay of the catalyst activity, how should the temperature be varied with time so that the total conversion over a fixed period of time is maximized? The solution to this problem is presented for reactors with various RTD's, and the effect of macromixing on the optimal policy is discussed. For reactors in segregated flow, with decay rate independent of conversion and a single irreversible reaction, the policy for any RTD is formed from three components: a stationary arc of constant conversion and two constrained arcs at the lower and upper temperature limits. In all but exceptional cases, the policy must end on the upper limit of temperature.By comparing the optimal average conversion in a single CSTR with that obtained by applying the optimal plug‐flow policy to the CSTR one can find the maximum loss in conversion to be suffered by using the optimal plug‐flow policy in a reactor of arbitrary, perhaps unknown, RTD. This loss was found in a numerical example to be negligible, which suggests that a reactor may be operated almost optimally without knowing its RTD.
Decomposition of sec‐butyl acetate on charcoal
Authors: Pettit P. J. , Anderson R. B. 
Published: March 2009

AbstractThe decomposition of sec‐butyl acetate on de‐ashed 20‐to 30‐mesh coconut‐shell charcoal (1500 m2/g) was studied in a fixed bed reactor in the temperature range 300–375°C, and at partial pressures of 1 atm. and 0.29 atm. The ester decomposed principally to n‐butene and acetic acid, and only small amounts of other products were found. The ratio of 1‐butene to 2‐butene was about 1:1, very close to that observed for thermal decomposition of the ester but far removed from the equilibrium butene ratio. The butene selectivity was independent of conversion.The rate of reaction followed the rate equationr = kA PE/1 + APEThis expression corresponds to surface reaction on one site being rate controlling. The activation energy of rate constant k was 32.7 kcal/mole, compared to 46.6 kcal/mole for the gas‐phase reaction. The temperature dependence of adsorption constant A showed a heat adsorption of 12 kcal/mole. Gas chromatographic measurements confirmed this value and also showed that ester is the principal adsor‐bate on the charcoal.
Model reduction of fixed bed catalytic reactors
Authors: McGreavy C. , Turner K. 
Published: March 2009

AbstractWith the increasing demand for optimal control and operation of plant, in particular chemical reactors, the need for detailed mathematical models which can be solved by computer in a reasonable time is apparent. Clearly, since the model is used repeatedly in each iteration of the computation, this will normally mean that it must be relatively simple. Unfortunately, this results in loss of detail necessary to take full advantage of the optimization.A technique for model reduction, suitable for the two‐dimensional heterogeneous catalytic reactor has been developed, which results in substantial reduction in dimensionality of the system, but which still retains the essential detail. Furthermore, it is possible to relate the well defined physical parameters, e.g. transport coefficients and rate constant, etc. to the parameters in the reduced model. Significant savings in computation time are made which makes it feasible to use the reduced model in optimization and control schemes.
Sulphur/halogen promoted oxidative dehydrogenation of hydrocarbons
Authors: Pasternak I. S. , Vadekar M. 
Published: March 2009

AbstractIodine is known to be an efficient promoter for the oxidative dehydrogenation of a wide variety of hydrocarbons. However, because of its high cost attempts have been made to reduce or eliminate it from the reaction system while still achieving high product yields.Theoretical considerations (thermodynamic and mechanistic) will be presented to show that it should be possible to use sulphur alone or together with chlorine and/or bromine in place of iodine or iodine/halogen mixtures in the oxidative dehydrogenation of different hydrocarbons. These considerations indicate that high product yields should also be possible with the new system if suitable catalysts are used.
H2S/Halogen promoted oxidative dehydrogenation of butene‐1
Authors: Vadekar M. , Pasternak I. S. 
Published: March 2009

AbstractAn experimental program was carried out to determine the effectiveness of H2S/mixed halogen promoters in the oxidative dehydrogenation reaction. Using the butene‐1 to butadiene reaction as an example it was found that while H2S or any of the hydrogen halides alone could be used as the promoter, superior conversions and selectivities (80–85%) were obtained when H2S was used in admixture with the halogens, preferably HCl and/or HBr. The effect of different catalysts and some processing variables (temperature, space velocity) on the desired reaction will be presented.
Selectivity of aging catalyst in static, moving and fluidized bed reactors
Authors: Campbell D. R. , Wojciechowski B. W. 
Published: March 2009

AbstractThe catalyst decay theory of Wojciechowski is applied to a simplified mechanism of catalytic gas oil cracking. The resulting patterns of selectivity predicted for a static bed reactor are presented in detail and general conclusions are drawn. It is shown that selectivity in gas oil cracking is bounded by optimum and minimum performance envelopes which confine the range of possible product distributions. For the simple cases considered, moving and fluidized bed reactors show selectivity patterns which invariably fall on the optimum performance envelope.
Entrance — region flow of viscoelastic fluids examined by means of jet thrust method
Authors: Oliver D. R. , MacSporran W. C. 
Published: March 2009

AbstractTube entrance‐region flow is examined by measuring the thrust of jets of liquid emerging from capillary tubes of different lengths. The liquids used are water, toluene, n‐pentanol and two aqueous polyacrylamide solutions possessing viscoelastic properties. The jet thrust behavior of each liquid is compared with the behavior calculated on the assumption that the liquid is Newtonian in character. Several facts emerge(a) the water behavior is near‐Newtonian.(b) for other liquids, the entry region is much more extensive than that predicted by Newtonian theory.(c) there is a striking peak in the jet thrust for intermediate values of L/D.(d) the steady state thrust levels are generally lower than those predicted by Newtonian theory.(e) for n‐pentanol and the more dilute polymer solution, these reduced thrust levels are consistent with previously published normal stress data.Possible reasons for the presence of a peak in jet thrust are discussed; this may well depend on shear elasticity possessed by the liquids. If so, the controversial suggestion that simple organic liquids possess shear elasticity is supported.It is shown that, in some cases, L/D ratios in excess of 350 are required for the establishment of steady laminar flow in the tubes.
Prediction of partial molal volumes of normal fluid mixtures
Authors: Chang Shinn‐Der , Lu Benjamin C.‐Y. 
Published: March 2009

AbstractPartial molal volumes of normal fluid mixtures in the liquid state were evaluated by means of a modified Redlich‐Kwong equation of state. Molal volumes and vapor pressures of pure saturated liquids were used for evaluating the two parameters of the equation. These parameters were treated as temperature dependent. Partial molal volumes of six binary systems were satisfactorily predicted in this investigation. Satisfactory compressibility factors for pure liquids at high pressures were also obtained by the proposed method.
Performance of tanks in series for non‐ideal mixing
Authors: Chiang David , Cholette A. 
Published: March 2009

AbstractThe performance of tanks in series, for imperfect mixing, is evaluated by resorting to a model characterized by two parameters, m and n, describing the level of mixing and the intensity of channeling or short‐circuit present in any one tank. An expression is obtained for the variation with time of the outlet concentration from the last tank, after subjecting the feed to a step change; it involves the summation of a number of terms, equal to the number of tanks in series, each term being the product of two expressions, the Binomial Probability Function and the Probability Integral of Chi‐Square Distribution, for which values are readily available in statistical and mathematical tables.When no short‐circuit is present, a single reading in the tables is required, whatever the number of tanks in series or the level of mixing; this includes perfect mixing, as a special case.For any given value of n, one family of curves is sufficient to correlate the variables, whatever may be the value of m or level of mixing. Five graphs depict clearly the overall influence of parameters m and n on the performance of reservoirs in series and can be used as working tools in many cases.
Time‐optimal output control computations for a class of linear tubular processes
Authors: Lim Henry C. 
Published: March 2009

AbstractTime‐optimal output control of a class of tubular processes described by partial differential equations is considered. A special transformation is used and the time‐optimal control is derived by using a lumped‐parameter theorem, thus circumventing computational complexity associated with distributed‐parameter systems. Time‐optimal controls are given for a number of examples, thin‐wall steam‐to‐fluid heat exchangers and single‐pipe heat exchangers with wall temperature and wall flux control. In some cases a bang‐bang control of a related lumped‐parameter process may be taken, for all practical purposes, as optimal, for example, a thin‐wall steam‐to‐air heat exchanger. However, in general, time optimal control is complex, requiring a bang‐bang control followed by an infinite number of switches between diminishing non‐extremal values.
Cascade control of a distributed parameter process
Authors: Campbell A. S. L. , Tinker E. B. 
Published: March 2009

AbstractThe application of cascade control to the regulation of outlet concentration of an isothermal, plug flow, tubular reactor, with first order reaction is considered. The optimum controller parameters and measurement point for the inner loop have been determined for distributed control and initial condition disturbance and vice versa. Optimum performance in both cases occurred with half the distributed lag in the inner loop. Cascade control showed considerable improvement in performance over that obtainable with a single loop system.
Distribution des temps de séjour et mélange maximal par un modèle de mélangeurs en cascade avec alimentation étagée
Authors: Villermaux J. 
Published: March 2009

AbstractThe maximum mixedness flow of fluid in a reactor is represented by a model of ideal mixers in a series provided with a stagewise feeding. This model enables to account for any RTD, to achieve the strict initial integration condition of the Zwietering differential equation, and to calculate by a new method the maximum mixedness conversion. A change of the variable is proposed which leads to a convenient representation of the integral trajectories. Although the strict initial integration condition depends on the infinite behavior of the intensity function, it is shown that the condition proposed by Zwietering gives in practice the best results.
Backmixing in a confined jet
Authors: Moeller W. G. , Dealy J. M. 
Published: March 2009

AbstractResidence time distributions in a circular confined jet were determined by monitoring the concentration in the outlet stream of a tracer which was injected into the primary jet. Both recirculatory and non‐recirculatory flows were studied, and the relationships between mixing parameters and the Craya‐Curtet number are presented. Some models for the mixing process are proposed.
A study of low shear viscosity of polymer melts
Authors: Chee K. K. , Rudin A. 
Published: March 2009

AbstractAn inexpensive, accurate falling coaxial cylinder viscometer is described. Viscosities can be measured at shear stresses at least as low as 103 dynes per cm2 and flow curves can be obtained with shear thinning fluids. Data for a polystyrene and a polyethylene polymer coincide with those from other techniques and with corresponding literature values. The lower Newtonian viscosities pf both polymers were experimentally accessible, and it is shown that estimation of ηo by extrapolation from viscosities in the non‐Newtonian region may be subject to errors of uncertain magnitude. Shear history of the sample affects the Newtonian and low shear viscosities of high molecular weight polymer melts.