bluuebunny/crossref_metadata_2025 huggingface dataset:
The activity of commercial water gas shift catalysts
Authors: Ruthven D. M.
Published: March 2009

Published kinetic data for commercial water gas shift catalysts are interpreted in terms of pore diffusional effects. The Arrhenius plots of apparent activity show the curvature typical of the transition from reaction to pore diffusion control and the apparent activities of different catalyst pellets vary quite widely. Effective diffusivity data are used to calculate intrinsic rate constants from the apparent activity data and it is found that the intrinsic activities of the catalysts considered are all similar. Furthermore the intrinsic activities, calculated in this way, give linear Arrhenius plots and activation energies which are in good agreement with values obtained experimentally using small catalyst particles (22–27 K. Cals). The effect of pressure on apparent catalyst activity is also discussed and it is shown that this effect may be accounted for satisfactorily by pore diffusional effects and it is not necessary to assume a change in the intrinsic rate equation at least at pressures below 20 atms.
The effect of baffle spacing on the dynamics of shell and tube heat exchangers
Authors: Chang D. R. C. , Tinker E. B.
Published: March 2009

This note reports on some aspects of the effect of shell side baffle geometry on the dynamic behaviour of flow forced shell and tube heat exchangers. Frequency response data for four heat exchangers with different baffle geometry were obtained. A second order critically damped transfer function gave an adequate description of the dynamic behaviour. The apparent natural frequency is a function of the shell‐side and tube‐side flow rates and fluid properties, as conveniently expressed by the overall heat transfer coefficient; and of the size and shape of the baffle compartments, as expressed by the ratio of shell diameter to baffle spacing.
Exact solution for diffusion to flow down an incline
Authors: Rotem Zeev , Neilson John E.
Published: March 2009

The concentration of solute in a film flowing down an inclined plane has been obtained by solving the complete diffusion equation, including the diffusion effect in the direction of flow. The formulation leads to the necessity of solving non‐orthogonal characteristic value problem, treatment of which is, however, quite straightforward.

Though the motivation for the study was the diffusion of oxygen to plasma or blood films, solutions are presented for the complete range of fluid properties, due to the great significance of this mode of flow for wider application in chemical engineering.
Minimum stable bubble volumes and bubble collapse rates in gas fluidized beds
Authors: Godard K. , Richardson J. F.
Published: March 2009

Measurements of the collapse rates of small bubbles injected into particulate gas fluidized beds show that the net transfer rate of gas from the bubbles to the continuous phase decreases as the background velocity is increased. The results indicate that the minimum stable bubble volume in a bed fluidized at a velocity equal to twice the minimum fluidizing velocity is 0.08 cc. Evidence of increase in the continuous phase voidage in the path followed by a bubble has been observed; this would explain the formation of stable bubble tracks.
Reactions of carbon vapor with a mixture of argon‐propane in a high intensity arc
Authors: Cholette A. , Covrtois P. A. , Parent J. R.
Published: March 2009

A high intensity arc reactor wag used to react carbon with a mixture of argon and propane at three different volumetric concentrations. The reaction output, when quenched, gives essentially C2H2, and hydrogen. The acetylene output depends mostly on the reaction temperature and on the carbon‐hydrogen ratio.

While higher concentrations of C2H2 might be obtained by operating the arc with a mixture of argon and propane rather than with pure propane, the efficiency of carbon utilization would be lowered when propane is diluted, the effect being more pronounced at higher concentrations of the diluent. The temperature of the carbon‐propane system is influenced to a small extent only by the presence of a diluent.
Scale‐up of continuous flow stirred tank reactors
Authors: Keairns D. L.
Published: March 2009

A model of a continuous flow stirred tank reactor based on laboratory experiments successfully describes the behavior of a pilot plant reactor. This model simulates the pilot plant performance over the full range of operating conditions: at high impeller speeds where performance approaches that of a perfectly mixed reactor and at low impeller speeds where performance significantly differs from perfect mixing. The micro‐mixed feed model divides the continuous flow stirred tank reactor into a small micro‐mixed impeller zone and a large macro‐mixer.
Continuous‐flow electrodialysis of acetate, butyrate, and chloride: A correlating equation
Authors: Schrodt J. Thomas , Yonikas Patrick J. , Grieves Robert B.
Published: March 2009

An experimental investigation is presented of the electrodialysis of acetate or butyrate with chloride, in a continuous‐flow unit with a membrane area of 50 cm.2 separating a test cell pair. The effects on the transport of the individual anions are established of several independent variables, including membrane type, organic specie, mole fraction of organic in the feed, and current density. Polarization is evident at a current density of 8 ma./cm.2

A semi‐empirical equation is developed and, utilizing the experimental data, the equation yields the cell constant and the ratio of the diffusivity of each anion to the film thickness. The equation, relating the purification factor (ratio of feed and effluent concentrations) and the key independent variables, may be utilized to correlate and extend a rather limited number of data points for other chemical systems in other continuous‐flow units.

For both membranes, both organic species, and over a wide range of feed mole fractions and current densities, the mole fraction of an anion transported across the membrane can be related to the feed mole fraction by a simple power relation, indicating a convenient way of expressing membrane selectivity.
Combined liquid‐ and vapor‐phase hydrocracking of heavy oil
Authors: Quinsey D. H. , Merrill W. H. , Herrmann W. A. O. , Pleet M. P.
Published: March 2009

A combined liquid and vapor‐phase pilot plant designed to hydrocrack heavy residues, pitches and bitumen containing high concentrations of nitrogen, sulphur and inorganic solid contaminants is described. Results are presented of preliminary experiments using the vacuum bottoms from Weyburn crude oil as a feed.
Gradient technique and lagrange multiplier – A technique for optimizing complex processes
Authors: Lee E. Stanley
Published: March 2009

The gradient technique combined with Lagrange multiplier is used to find the optimum of a complex heterogeneous process with two recycle streams. Both the reaction stages and the separation stages for the separation of a six component mixture are considered. In spite of the complexity of the process, only two minutes computation (IBM 7094) is needed to obtain the solution. Techniques for handling inequality constraints on the control and state variables are also discussed.
Design of differential countercurrent extractors with backmixing using stagewise models
Authors: Mecklenburgh J. C. , Hartland S.
Published: March 2009

Methods are presented which enable the behavior of a differential contactor with backmixing to be estimated from that of a stagewise model with equivalent backmixing. The latter requires fewer stages than the models previously proposed. The inherent instability of the equations renders the boundary iteration method of solving the stagewise equations unreliable. However, this instability may be avoided by simultaneous solution of the equations and furthermore it is possible to reduce the amount of computer storage required if an unsteady state method is used.
The growth and dissolution of potassium sulphate crystals in a fluidized bed crystallizer
Authors: Mullin J. W. , Gaska C.
Published: March 2009

The nucleation, growth and dissolution characteristics of potassium sulphate have been studied in a laboratory scale fluidized bed crystallizer under carefully controlled conditions of temperature, supersaturation and solution velocity. Aqueous solutions of potassium sulphate can withstand high degrees of supercooling (∼ 13°C) even when agitated, but this is reduced to about 5°C when the crystalline phase is present. Nevertheless, this is still a high level of supercooling for an aqueous salt solution. The importance of measuring nucleation data for crystallizer design purposes under the appropriate conditions is clearly demonstrated.

The ‘order’ of the nucleation process, m, defined by Rn = KnΔcm is about 9. The growth process, defined by Rg = KgΔcn is second‐order (n = 2) with an activation energy of 4.3 kcal/mole, and the dissolution process, Rd = KdΔcp, in first‐order (p = 1) with an activation energy of 3.4 kcal/mole.

The growth step is therefore considered to be diffusion controlled, and this is confirmed by the observation that the growth rate of potassium sulphate in a fluidized bed is dependent on the size of the crystals.
Group contributions in vapor‐liquid equilibrium
Authors: Rodger Alan J. , Hsu Cheng C. , Furter William F.
Published: March 2009

An empirical method has been developed for the prediction of vapor‐liquid equilibrium data, both composition and temperature, for a series of binaries of chain hydrocarbons with carbon tetrachloride. The maximum and absolute average deviations in vapor composition are 0.035 and 0.006 mole fraction, respectively, and in temperature are 1.5 and 0.4°C, respectively. Because of assumptions inherent in the theory, the prediction (as opposed to correlation) tends to apply only with chain compounds and not with compounds containing rings. Systems containing cyclic and aromatic hydrocarbon compounds, however, have been correlated by this method with some degree of success.
The quasi‐steady‐state approximation in continuous stirred tank reactors
Authors: Ray W. H.
Published: March 2009

The Quasi‐steady‐state‐approximation (QSSA) applied lo continuous stirred tank reactors (CSTR) is examined. The induction period is found to be somewhat longer and the error in the QSSA larger than for batch reactors. This error is usually insignificant except when CSTR conversions are low. An alternative approximation is proposed for this case. The errors in the QSSA are also illustrated for the well known cases of Enzyme and Free‐Radical polymerization kinetics.
Kinetic energy and momentum factors for rough pipes
Authors: Booth Robin G. , Epstein Norman
Published: March 2009

Kinetic energy and momentum factors are derived, evaluated and presented for fully developed turbulent flow in both uniformly sand‐roughened and commercial pipes as a function of Reynolds number and relative roughness. For the uniform sand roughness, the universal velocity profile and friction factor equations of Nedderman and Shearer were used, while for the commercial roughness the corresponding equations of Colebrook and White were employed.
Temperature distributions in a helium plasma
Authors: Meubus P. , Parent J. R.
Published: March 2009

Temperature distributions are determined in a helium plasma, the power used being 27 kW and the gas flow rate 7.2 g/minute. Pressure conditions for the plasma under study are respectively 760 and 300 mm Hg.

The spectroscopic method used for obtaining temperatures is that of Larenz or the method of maximum emission, applied to the 3,889 Å neutral helium line. A maximum temperature, on the plasma axis, of approximately 24,000° K is obtained.
Velocity distributions in a gaseous plasma: I. Derivation of flow types within a helium plasma
Authors: Meubus P. , Parent J. R.
Published: March 2009

Velocity distributions in a plasma jet are generally determined by means of direct methods which are liable to alter the medium, especially at very high temperatures. A gas flow model is proposed, which is worked out from the luminous profile of a helium plasma jet, such as viewed through a dense orange glass filter. The knowledge of the luminous profile equation, temperature distribution, gas flow rate and energy balance completely determine the velocity distribution in the plasma. Boundary conditions lead, in certain cases, to the concept of an axial turbulent core. The helium plasma was operated at 27 kW, with a gas flow rate of 7.2 g/minute. The jet was issuing into an atmosphere kept at 300 mm Hg in order to favor conditions leading to laminar flow.
Experimental study of natural convection heat transfer from a vertical plate in a non‐newtonian fluid
Authors: Sharma K. K. , Adelman Maurice
Published: March 2009

An experimental investigation of natural convection heat transfer to non‐Newtonian fluids from isothermal vertical plates was carried out. Three aqueous solutions of Carbopol 934 (1.25%, 1.5% and 1.75%) were selected as pseudoplastic fluids providing a flow behavior index range from 0.2 to 0.67. All the experimental data lay in the laminar flow range (NGrNPr < 109). A successful correlation for predicting natural convective heat transfer coefficients for non‐Newtonian fluids from flow behavior index 0.2 to 1.0 inclusive was developed.
Experimental study of natural convection heat transfer in a non‐newtonian fluid: Part II. Horizontal plate
Authors: Sharma K. K. , Adelman Maurice
Published: March 2009

Experimental data on natural convection heat transfer to non‐Newtonian fluids from isothermal horizontal flat plates facing both up and down are reported. Emperical expressions for predicting the heat transfer coefficient for fluids as the flow behavior index is varied from 0.19 to 1.0 were developed. These are essentially similar to the vertical plate case and correlate the data with reasonable accuracy.
Mass transfer from a single rising bubble
Authors: Johnson A. I. , Besik F. , Hamielec A. E.
Published: March 2009

The absorption rates of carbon dioxide, ethylene, and butene from single rising bubble of equivalent diameter 0.4–2.0 cm in water have been measured using an apparatus in which the bubble volume change with time of rise can be measured. The apparatus uses techniques previously reported but also is suitable for studies of mass transfer without and with chemical reaction at higher pressures (up to 4 atmospheres). The results have been compared with theoretical equations for rate of gas solution at the frontal surface of the bubble based upon potential flow theory and Higbie theory.

The data are assessed together with those of others to show that they can be correlated well by

This equation is valid for bubbles of equivalent diameter 0.6 < d < 4.0 cm and within the range

500 < NRe < 20,000
The dynamics of extraction processes: Part II. Comparison of dynamic testing methods and their application to an extraction process
Authors: Pollock G. G. , Johnson A. I.
Published: March 2009

A comparison of the theoretical and experimental difficulties and advantages of sinusoidal, pulse, and step testing procedures, as applied to a continuous stagewise extraction process, is made.

An experimental extraction apparatus suitable for a variety of dynamic studies is described. For this apparatus step testing has been found to give results as reliable as those from pulse methods.

The paper develops the theoretical background and describes experimental implementation of double pulse testing.

The extraction column when used with the system water‐acetic acid‐methyl isobutyl ketone was found to behave linearly over the range of variables studied. The stages of the column were found to be “well‐mixed”, and it was concluded that the column could be best represented by a lumped parameter model.
Studies on yield in gas‐liquid contacting reactors
Authors: Ohki Yoshihiro , Inoue Hakuai
Published: March 2009

Analytical solutions giving the yield of a first order consecutive reaction in a gas‐liquid contacting reactor are derived for cocurrent, countercurrent plug flow and perfectly mixed flow systems. The general solutions derived from the consideration of both reaction and transfer processes by a new mathematical method clarify the effect of mass transfer rate on the yield. Special solutions with the condition of infinite mass transfer rates can be used to choose the best flow system and to calculate the operating conditions for the greatest reactor yield.
The optimal control of polymerisation reactors
Authors: Hicks James , Mohan Amar , Ray W. Harmon
Published: March 2009

Two 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

Leg 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

The 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

A 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

The 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

Various 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

Given 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

A 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

Rational 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

A 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

The 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

The 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

The 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 equation

r = kA PE/1 + APE

This 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

With 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

Iodine 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

An 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

The 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

Tube 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

Partial 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

The 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

Time‐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

The 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

The 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.
Forced convection heat transfer in narrow passages
Authors: James P. A.
Published: March 2009

A simple analysis of heat transfer in narrow ducts is derived, with application to a fluid in laminar flow through an elliptical duct of high aspect ratio. A solution to the latter problem for aspect ratios in the range 1.0 to 100 is also presented.
Backmixing in a confined jet
Authors: Moeller W. G. , Dealy J. M.
Published: March 2009

Residence 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

An 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.
Bubble formation in viscous liquids under constant flow conditions
Authors: Kumar R. , Kuloor N. R.
Published: March 2009

Bubble formation from single nozzles has been studied in liquids of different viscosities. The viscosity is varied in the range 50 to 500 c.p., whereas flow rates up to 100 cm3/second have been investigated. A model based on a two step (viz. expansion and detachment) mechanism has been proposed for bubble formation. The model explains the results of the present investigation as well as those reported in the literature for similar systems. As an extreme case, the model is tested on liquids of very low viscosity after dropping the viscosity terms from the equations and is found to explain even these data quite well.
Transport phenomena under unsteady conditions in an agitated vessel
Authors: Rajan V. S. V. , Picot J. J. C.
Published: March 2009

An experimental study of transport phenomena at the wall of an agitated vessel with a propeller impeller under unsteady conditions is reported. The transient in heat transfer at the wall is caused by a step change in the speed of agitation from an initial static condition. The results are expressed in terms of a rise in modified “j‐factor” above the initial free convection value and the number of revolutions taken by the impeller from the start of agitation. Also, an attempt has been made to find an analogy beween heat and momentum transfer. Results are given for the power in terms of Euler number plotted against the impeller Reynolds number. An empirical expression is also given for the transient heat transfer considering the system as a pure first order one with time delay. A “time‐factor” constant which gives the number of impeller revolutions for 63.2% of the change from the initial to a final steady state is expressed as a function of impeller Reynolds number (102 to 106) and fluid Prandtl number (6 to 106).
The accuracy of kinetic parameters estimated from batch and integral reactor data
Authors: Ravimohan A. L. , Chen W. H. , Seinfeld J. H.
Published: March 2009

The accuracy of rate constant estimates obtained by minimizing the sum of squares of differences between observed and calculated concentrations is considered. Closed solutions are obtained for some basic types of first order reaction schemes. The results are presented in the form of plots of the dimensionless variance of parameter estimates. The kineticist can use the plots both in analyzing experiments and in planning them for maximum economy. Such advance studies are capable of providing valuable insight into questions of experimental design even when the reaction scheme is unknown.
Langmuir‐temkin‐pyzhev rate models for ammonia decomposition reaction
Authors: Takezawa Nobutsune , Mezaki Reiji
Published: March 2009

Existing rate data of ammonia decomposition were correlated using the Langmuir‐Temkin‐Pyzhev models and the applicability of those models was examined. Conventional statistical tests indicated that the Langmuir‐Temkin‐Pyzhev model was adequate, but the physico‐chemical examination of parameter estimates showed that the model was not feasible. The Temkin‐Pyzhev model was also employed to describe the decomposition data and discussed.
Transport properties of simple non polar binary liquid mixtures
Authors: Brunet J. , Doan M. H.
Published: March 2009

Theorems of corresponding states for predicting the temperature and density dependence of liquid mixture transport properties are presented. The technique is tested for thirteen systems of spherical molecules (eight cryogenic mixtures, and five others) in which viscosity is predicted within 3%. For cryogenic mixtures, temperatures range from the triple point to temperatures close to the critical. In the present method, the only quantities required are pair potential parameters between like pair interactions, as determined from gas phase viscosity measurements, and pure component data.

The lack of accurate measurements of thermal conductivity and diffusivity (mutual or self diffusion coefficients) for mixtures of spherical molecules(1) does not make it possible to test the present theory of those transport properties.
An improved method for numerical solution of distillation processes
Authors: Gentry James W.
Published: March 2009

A new method for the numerical solution of a stagewise process is presented. The method consists of total linearization of all the equations in the distillation process, using the method of quasi‐linearization. The resulting equations form a block‐band matrix which can be readily solved by a method developed by the author. The method used for obtaining convergence is presented.

The method has been tested for both binary and multi‐component systems. The method has been compared with the Amundson‐Pontinen method for a five component mixture. The method gives more rapid convergence. Numerical experiments indicate that the vapor and liquid flow rates are more stringent requirements than the bubble point.
Continuous flow mixing of two miscible liquids of different densities
Authors: Pelletier Martin , Cloutier Leonce
Published: March 2009

Positive step demands hsve been used to study the behavior of miscible liquids with different densities in an imperfectly mixed cylinderical flow tank. A model was elaborated to predict the response of the agiated system. Comparisons between experimental and theoritical results have shown the limits of the proposed model and equations.
Turbulence parameters in a stirred tank
Authors: Mujumdar A. S. , Huang B. , Wolf D. , Weber M. E. , Douglas W. J. M.
Published: March 2009

Mean and fluctuating radial velocities have been measured in the inipeller stream of a baffled, turbine‐agitated cylindrical tank. Auto‐correlation functions, energy spectra and amplitude probabilitv density functions of the radial velocity fluctuations were also obtained. In the vicinity of the impeller, the motion is distinctly periodic, with a time scale corresponding to nbN/60, where nb is the number of turbine blades and N is the rpm. The amplitude of the periodic component was found to decrease with radial distance from the inipeller tip and was used to correct the measured turbulence intensities.
Transition phenomena in an oscillating manometer
Authors: Park J. R. S. , Baird M. H. I.
Published: March 2009

The decay of oscillation of a liquid column in a manometer has been studied. Measured values of the damping coefficients in laminar conditions agree well with previous data. The transition between turbulent and laminar damping has also been measured. For transition to fully developed turbulent flow, the critical Reynolds number is a function only of the Valensi number. In situations where turbulence exists at the ends of the liquid column but laminar conditions persist in the main section, the transition Reynolds number and damping exponent are functions of frequency and kinematic viscosity as well as Valensi number.
Gibbs free energy and activity coefficients from total pressure measurements
Authors: Minh D. C. , Rvel M.
Published: March 2009

Improvements of an existing method for the calculation of the Gibbs free energy and activity coefficients for binary non‐ideal solutions from total pressure measurements are presented. These improvements are particularly significant whenever the ratio of the vapor pressures of the pure components is greater than 10. The convergence is rapid and the method is well adapted to digital computation.