Showing papers in "Chemical Engineering Science in 1970"

A structural model for gas—solid reactions with a moving boundary

Abstract: Gas—solid reactions involving a moving boundary are generally described in terms of the shrinking core model, where structural parameters are incorporated into an empirical reaction rate constant. ln the paper an alternative representation is proposed by describing the progress of the reaction in terms of the porosity, grain size, gas phase and solid state diffusivities and a heterogeneous reaction rate constant, which is now independent of structure. By taking “reasonable values” for these parameters the model was found to reproduce the general trends exhibited by the experimental data of other investigators.

Longitudinal mixing of the liquid phase in bubble columns

Abstract: Longitudinal dispersion coefficient was measured in batch type bubble columns of 40, 80 and 160 mm diameter with perforated plates. Models were established to interpret the behaviour of the coefficient. For the bubble flow condition at low gas flow rate, the model with the consideration of combined action of the velocity profile and the bubble motion was developed from Taylor's theory. For the coalesced bubble-slug flow condition at high flow rates, the expansion model was proposed on the basis of the actual dispersion coefficient in liquid phase which was separated from the apparent value. Both models showed a good agreement with the experimental data of many investigators.

Mechanics and mass transfer of single bubbles in free rise through some Newtonian and non-Newtonian liquids

Abstract: A “constant volume” technique is described for measuring the instantaneous rates of solution of rising gas bubbles in liquids; this simultaneously determines the bubble shape, area and rising velocity at the instant of measurement. The method has been tested using carbon dioxide bubbles in water and is seen to give excellent results which have been extended to include carbon dioxide bubbles in two viscous Newtonian aqueous solutions of glycerol and in a non-Newtonian viscoelastic pseudoplastic aqueous solution of polyethylene oxide (“polyox”). Results covering a wide range of bubble sizes (0·2–6·0 cm equivalent spherical diameter) are reported. The observed changes in bubble shape with size in each liquid are documented, and detailed comparisons of the collected data with existing theoretical models relating to bubble rise velocity and overall mass transfer coefficient are carried out. A new theory for mass transfer in the bubble wake is developed and found to agree with observation to a first approximation.

Parametric sensitivity and runaway in fixed bed catalytic reactors

Abstract: The paper introduces two intrinsic criteria for runaway in fixed bed tubular reactors based on the occurrence of characteristic points in the temperature profile along the reactor. Their transposition in the partial pressure-temperature phase plane allows the derivation of some very simple formulae for the prediction of the critical values for the operating variables. The results are compared with those obtained from Barkelew's empirical criterion. The paper also treats the related problem of a hot spot ehich has to be limited for reasons after the runaway. The simple formulae mentioned above can also be used in this case to determine the operating conditions.

Theoretical prediction of the sizes of drops formed in the breakup of capillary jets

Abstract: The breaking up of a liquid jet subject to small disturbances was studied experimentally and theoretically. A non-linear theory was used to calculate the profile of the waves on the surface of the jet at breakup, and also to predict the volume of the main and satellite drops. It was found that the theoretical and experimental drop volumes were in good agreement. However, satellites were observed in all experiments whereas the theory predicts that satellites should not form for dimensionless wavenumbers greater than 0·7. In the experiments it was not possible to make the jets break up into single main drops of uniform size. The results suggest that it may be possible to produce uniformly sized drops if the main and satellite drops have the same volume.

Modeling of chemical reactors — XVI Steady state axial heat and mass transfer in tubular reactors An analysis of the uniqueness of solutions

Abstract: Numerical methods for the solution of steady state equations are reviewed and critically discussed. A new technique is presented which, for the parameter study of a problem, enables one to transform the boundary value problem to the initial value problem. Different criteria for testing of uniqueness and multiplicity respectively are discussed. The necessary and sufficient conditions of multiplicity and also analytical procedures providing an estimate of bounds of the Damkohler numbers where multiple solutions can occur, are presented. The mentioned criteria are presented for both an adiabatic and nonisothermal-nonadiabatic case.

Irreducible wetting-phase saturations in porous media

Abstract: The irreducible wetting phase saturation retained by drained porous solid has been investigated systematically. Changes in the variables interfacial tension, viscosity, fluid density, viscoelasticity, contact angle, mixed wettability, particle shape, pore shape, permeability, porosity and particle size distribution were found to have little influence, per se , on the magnitude of the irreducible saturations, which usually fell in the range of 6 to 10 per cent of the pore space. The much higher irreducible saturations commonly observed in practice, can be obtained in the laboratory with a variety of suitably arranged heterogenous packings. These were made by placing cluster of fine particles in a matrix of coarse particles. Water remains trapped in the particle regions because these regions lose hydraulic continuity through the media before the applied capillary pressure is sufficient to effect drainage. It is concluded that the magnitude of irreducible wetting phase saturations is dominated by heterogeneity of pore structure.

Shock waves as a criterion for the transition from homogeneous to heterogeneous fluidization

Abstract: The transition from homogeneous to heterogeneous fluidization is described by the occurrence of shock waves. Shock waves will arise in a fluidized bed when the rising velocity of a porosity fluctuation exceeds the longitudinal propagation velocity of an equilibrium disturbance. An expression for the latter velocity has been derived via the elastic properties of a fluidized system. The elasticity modulus of this system has been calculated from a drag force-interparticle distance relation. It is shown that along these lines a satisfactory criterion for the transition between homogeneous and heterogeneous fluidization has been obtained.

The interpretation of residence-time experiments

Abstract: The results of tracer experiments can depend on the methods of injection and measurement of the tracer when the fluid velocity is not uniform through the injection and measurement planes. Some simple examples show that incorrect residence-time distributions will be derived if this fact is not considered. For laminar flow in a tube the results obtained will differ widely, depending on the techniques used.

The stability of steady shear flows of some viscoelastic fluids

Abstract: The stability of steady shear flows of some viscoelastic fluids relative to small perturbations in the initial data is examined. It is shown that all values of the steady shear rate where the flow curve exhibits a zero or negative slope the flow is unstable. This conclusion is corroborated by existing experimental data and bears upon the phenomenon of melt fracture.

The kinetics of oxidation of aqueous sodium sulphite solution

Abstract: The kinetic data of the reaction were calculated from the absorption rate of oxygen into the mechanically agitated sulphite solutions It was found that the reaction order in oxygen depends on the oxygen concentration in the liquid phase at the interface The reaction is first order for oxygen concentrations higher than approximately 6 10−4 kmol m−3 at the interface and second order for lower oxygen concentrations The relation between first order reaction rate constant, temperature and pH-value of the solution and cobalt catalyst concentration is presented for sulphite solutions prepared in two different ways The influence of the purity of the sulphite solutions upon the values of constants involved in the kinetic equation was studied The authors do not recommend taking the rate data of the reaction from the literature because the quoted constants depend on the purity of the solution

Properties of bubbles in three phase fluidized beds as measured by an electroresistivity probe

Abstract: Measurements of local bubble properties in a gas—liquid fluidized bed have been made using an electroresistivity probe. The probe data were analyzed with a hybrid computer using the techniques applied by Park et. al. to gas fluidized beds. Results are reported for the variation of bubble frequency, volume fraction, size and size distribution, and rising velocity as a function of fluidization level, particle size and position within the bed. The bubble size and rising velocity size and rising velocity were correlated in terms of the overall bed porosity. Bed viscosity was also measured to assess its effect on bubble velocity. A comparison of the present data has been made with the available literature.

Gas absorption accompanied by complex chemical reactions- I Reversible chemical reactions

Abstract: A solution based on the film theory is presented for gas absorption accompanied by a generalized, reversible chemical reaction of the form γAA+γBB⇋γEE+γFF. The approximate solution for the ratio of mass transfer coefficients, Φ, is derived and compared graphically with the exact numerical solutions for several limiting cases. It is shown that the error of this approximate method is less than several per cent.

Salt rejection phenomena in the freezing of saline solutions

Abstract: The salt redistribution process occurring in the freezing of a NaCl solution was examined, and the factors responsible for controlling salt rejection were analyzed. One-dimensional freezing of NaCl solutions ranging in concentration from 0·005–0·10 N was carried out vertically in a thermally insulated test cell. A new experimental approach to measuring the liquid phase solute distribution used microconductance probes fixed at stationary points in the test cell. The conductance probes, developed by these authors, had a resolution of 20 μ and provided, for the first time, a method for monitoring the NaCl-rich boundary layer developed adjacent to the advancing solid—liquid interface. The solute boundary layer thickness was observed to vary inversely with the freezing rate and ranged from approximately 60–600 μ for freezing rates ranging 45-4 μ/sec. The ratio of the liquid phase concentration at the interface to the bulk concentration varied inversely with the bulk concentration and thermal driving force, and in each case, this ratio attained the critical value predicted from theory to denote the onset of constitutional supercooling. Two parameters were found to control the redistribution process: (1) the liquid phase interface concentration which is controlled by constitutional supercooling, and and (2) the thermal driving force imposed on the system to initiate and maintain freezing. Once these two parameters are specified, an overall mass balance requires that the resulting solid phase concentration be uniquely determined. These findings contradict theories reported by other authors who believe that rejection is controlled by a distribution coefficient which is solely a function of the freezing rate. This investigation shows such a distribution coefficient to be only an indirect function of the freezing rate. It was found to be a passive parameter that merely describes,not controls, the redistribution of salt.

An analysis of adiabatic sorption of single solutes in fixed beds: pure thermal wave formation and its practical implications

Abstract: Concentration and temperature profiles arising in adiabatic fixed-bed adsorption of a single gaseous component are analyzed, with particular reference to the special case of a pure temperature wave preceding the mass transfer zone. A simple approximate criterion for its existence under practical conditions is presented which is met by many systems of industrial importance. It is further shown and verified by experiment that the solute breakthrough time will in this case be independent of the initial bed temperature. The results lead to the important conclusion that the usual cooling step following the thermal regeneration of a bed may be omitted in such systems without appreciably affecting the adsorber performance.

On membrane diffusion with near-equilibrium reaction

Abstract: An analysis is presented of the "facilitated" transport problem, involving steady diffusion through a finite membrane, accompanied by rapid and reversible, homogeneous chemical reaction. For the limit of infinitely fast reactions, the method of matched asymptotic expansions is used to analyze the asymptotic structure of the diffusion field, which is shown to consist of an "equilibrium core," together with "boundary-layer" reaction zones at the membrane boundaries. Asymptotic expansions are derived, which would in principle allow one to compute both the first- and second-order effects of departure from reaction equilibrium on the net rates of diffusion mass transfer. Several examples are considered, one of which is a model of oxygen diffusion through hemoglobin solutions, and some comparisons with analytical and numerical solutions are given.

Modeling of chemical reactors — XVII Steady state axial heat and mass transfer in tubular reactors Numerical investigation of multiplicity

Abstract: Numerical results are presented in graphical form for a range of parameters where multiple solutions may occur. These results provide valuable material for a further theoretical examination of multiplicity. It is also shown that in multiple cases the Danckwerts boundary conditions are consistent with stirred tank and piston flow respectively. Possibilities of an existence of multiplicity at high Peclet numbers are discussed. On the base of a simple analysis an estimation of the coordinates of a trifurcation point is developed, which together with a range of Damkohler numbers were multiplicity can occur are compared with the exact values. It is shown that these criteria are remarkably good. A discussion of the effects of axial mixing in the industrial adiabatic packed beds is presented.

Gas absorption accompanied by complex chemical reactions — III Parallel chemical reactions

Abstract: Gas absorption accompanied by the parallel chemical reactions is discussed from the view-point of the film theory. The approximate solutions for the ratio Φ are derived by the same method described in our previous papers and compared with the analytical or numerical solutions for several cases. The difference of the ratio Φ between the approximate and the exact solutions is only a few per cent.

Modeling of chemical reactors—XVIII stability and oscillatory behaviour of the CSTR

Abstract: In this paper mass and enthalpy balances for a homogeneous CSTR with recirculation of both heat and mass have been written An analysis of these equations is performed and necessary and sufficient conditions for multiplicity are developed These conditions are consistent with previously obtained results For highly exothermic reactions being carried out in nonisothermal-nonadiabatic CSTR which are “overcooled” the effect of “over-cooling” is discussed On the basis of a closed curve in a plane “temperature—residence time”, sometimes called isola, one may show that such reactors cannot be autothermally ignited The case where two extinction points and no ignition point exist as well as a case when two ignition points plus two extinction points occur will be discussed It is shown that if an adiabatic temperature riseB is increased, the occurence of an isola is shifted towards higher values of the dimensionless heat transfer coefficient β A number of diagrams for different combinations of parameters are presented where regions of multiplicity are reported A new procedure is described making it possible to locate easily limit cycles as well as multiplicity and, in addition, to classify stability of singular points in question This approach is based upon determination of the behaviour of singular points inside domains being cut by two families of curves—locus of saddle point and locus of “transient instability”—in a plane “Damkohler number Da vs adiabatic temperature rise B” A simple way of classifying these domains is described A necessary condition for a limit cycle surrounding a stable singular point is developed In the diagrams “Da—B” the regions are characterized where this limit cycle may be expected These diagrams seem to be an appropriate aid for a dynamic analysis of nonlinear reacting systems because they enable one to discover phenomena which formerly could be discovered only more difficult, eg three singular points in a single limit cycle etc In diesem Artikel werden Stoff- und Enthalpiebilanzen fur einen homogenen CSTR mit Warme sowie Stoffaustausch beschrieben Es wird eine Analyse dieser Gleichungen durchgefuhrt und die fur Multiplizitat notwendigen und hinreichenden Bedingungen werden entwickelt Diese Bedingungen stimmen mit den fruher erhaltenen Ergebnissen uberein Fur stark exotherme Reaktionen, die in nichtisothermischen nichtadiabatischen CSTR ausgefuhrt werden, der “uberkuhlt” wird, wird die Wirkung der “Uberkulung” erortert Auf Grund einer geschlossenen Kurve in einer “Temperatur-Verweilzeit” Ebene, manchmal Isola genannt, kann gezeigt werden, dass derartige Reaktoren nicht autothermisch ilzundet werden konnen Der Fall, wo zwei Loschpunkte und kein Zundpunkt vorhanden sind, sowie ein Fall mit zwei Zundpunkten und zwei Loschpunkten werden besprochen Es wird gezeigt, dass bei Vergrosserung einer adiabatischen Temperaturerhohung B das Vorkommen einer Isola gegen hohere Werte des dimensionslosen Warmeu bertragungskoeffizienten β verschoben wird Es wird eine Reihe von Diagrammen fur verschiedene Kombinationen von Parametern wo Gebiete von Multiplizitat auftreten dargelegt Eine neue Methode wird beschrieben, mit welcher es leicht moglich ist Grenzzykle sowie Multiphzitat testzustenen und daruber hinaus die Stabilitat in Frage kommender Einzelpunkte zu beurteilen Dieses Verfahren beruht auf der Bestimmung des Verhaltens von Einzelpunkten innerhalb von durch zwei Kurvenscharen geschnittenen Bereichen—geometrischer Ort des Sattelpunktes und geometrischer Ort der “instationaren Instabilitat” —in einer “Damkohlersche Zahl Da gegen adiabatischen Temperaturanstieg B” Ebene Es wird ein einfacher Weg zur Beurteilung dieser Bereiche beschrieben Es wird eine notwendige Bedingung fur einen Grenzzyklus um einen stabilen Einzelpunkt entwickelt In den Diagrammen “Da—B” werden die Gebiete gekennzeichnet wo dieser Grenzzyklus erwartet werden kann Diese Diagramme scheinen eine geeignete Hilfe fur eine dynamische Analyse nichtlinearer Reaktionssysteme darzustellen weil sie es ermoglichen Erscheinungen zu entdecken deren Auftreten fruher nur mit Schwierigkeiten entdeckt werden konnte, zB drei Finzelpunkte in einem einzigen Grenzzyklus usw

High capillary number withdrawal from viscous Newtonian liquids by flat plates

Abstract: This paper proposes a new theory for withdrawal from viscous Newtonian liquids by vertical plates. The thickness of the liquid layer on the withdrawn plate was determined experimentally by a light adsorption method. Theory and experiments both indicate that the maximum possible thickness is not realised in cases where the action of the capillary pressure of the meniscus can be neglected. The realised flux is 17 per cent lower than the maximum flux.

A theory of constant pressure filtration

Abstract: Attention is drawn to two equivalent analyses that describe the one dimensional process of “cake” filtration. These analyses, which arise from conventional theory of flow of fluid in porous media, permit the prediction of density gradients in the solid material at any time, as it accumulates on the filter membrane, and may be used to predict conditions that should be imposed to achieve greatest efficiency in the filtration process.

Coupling between diffusion and convection in radial dispersion of matter by fluid flow through packed beds

Abstract: It is shown, both theoretically and by means of literature data, that coupling between diffusion and convection does not only occur in longitudinal dispersion of matter by fluid flow through packed beds (in which it is already known to occur) but also in radial dispersion.

Gas exchange between the bubble and emulsion phases in gas-solid fluidized beds

Abstract: Experimental studies for measuring the extent of gas exchange between the bubble and emulsion phases in gas-solid fluidized beds were conducted using ozone as a tracer. Measurements were made on tha changes of ozone concentration immediately inside the bubbles which were injected successively into the incipiently air fluidized bed. Exchange coefficients thus obtained were compared with those predicted theoretically and were found to be in good agreement. It was concluded from these results that the model used in this study based on the diffusional gas exchange between clouds and the emulsion phase was reasonable. The exchange coefficient values measured for single bubbles, as seen in this study, were found to be roughly one third of that obtained from freely bubbling fluidized beds, which fact was attributed to the coalescence of bubbles in the freely bubbling beds. The effect of gas adsorption on the surface of the particles was estimated and discussed.

A model of the mechanism of transport in packed, distended, and fluidized beds

Abstract: An instrumented copper sphere, 1·5 in. in dia., was provided with a small calorimeter which permitted measurements of the local thermal transfer within a packed bed of spheres of uniform diameter. A 12 in. dia., 20 in. long column packed with 1·5 in. spheres in a rhombohedral number six, blocked passage array was employed to study the local thermal transport as the result of the steady flow of air over a range of superficial Reynolds numbers from 875 to 3618. A boundary layer model based upon the established behavior of thermal and material transfer from single cylinders and spheres in turbulent fluid streams is discussed. Local air velocity in the flow passages was measured directly. A characteristic turbulence intensity within the flow passage was established from the local thermal transfer measurements and was found to agree with direct “hot- wire” measurements. The model provides an analytic expression which was found to represent transport from single cylinders and spheres, and arrays of cylindrical, spherical, and commercial packing. In addition, the model applies to distended and fluidized beds of spherical particles. The over-all deviation was 9·8 per cent for the various types of packed arrays. This model predicted the height of a gas phase transfer unit in commercial packed columns being irrigated with liquid within 12 per cent for twelve cases involving both absorption and vaporization.

The use of residence time distribution data for estimation of parameters in the axial dispersion model

Abstract: In this paper are presented four convenient methods for determination of the mean residence time and the axial dispersion coefficient of a flow system by analysis of data obtained by means of the imperfect tracer pulse method. The analysis is based upon numerical evaluation of the transfer function and its derivatives for a number of values of the Laplace transform parameter, Sτ .

Response modes of continuous stirred tank reactors

Abstract: The general applicability of stoichiometric constraints to reduce the dimensions of the differential equations describing the process dynamics of continuous stirred tank reactors has been disputed in the literature, and attempts have been made to disprove it. However, it turns out that the fundamental stoichiometric constraints on a set of chemical reactions carry over to the dynamics of open systems in the analysis of asymptomatic stability. In fact, the stoichiometric constraint becomes a new combined state variable, a general asymptomatic invariant, which is invariant to the way the chemical reactions proceed. Hence, only a reduced set of the stirred tank eigenvalues is changed by the reactions. The dimension of this set is equal to the number of independent reactions, also when temperature is included in the state vector. The remaining eigenvalues are left unchanged as if no reaction takes place. For global analysis, however, the reaction is valid only in the very special case when the initial conditions of the chemical species and the feed concentration vector obey the stoichiometric constraint.

Tracer curves and the residence time distribution

Abstract: For a pulse input the shape of the output tracer curve depends on the way tracer is distributed across the flowing fluid, and the way it is measured. This paper properly relates the different curves which may be obtained for flows with negligible cross diffusion, and shows which one of these represents directly the residence time distribution of the flowing fluid.

Transport properties of porous lime and their influence on the decomposition of porous compacts of calcium carbonate

Abstract: Special experimental techniques have been developed to measure the thermal conductivity of porous lime and the diffusion coefficient of carbon dioxide through it. Measurements have been made on lime whose porosity varied in the range 0·45