Showing papers in "Chemical Engineering Science in 1984"

Autocatalytic reactions in the isothermal, continuous stirred tank reactor: Oscillations and instabilities in the system A + 2B → 3B; B → C

Abstract: The prototype, cubic autocatalytic reaction (A + 2B → 3B) forms the basis for the simplest homogeneous system to display “exotic” behaviour Even under well-stirred, isothermal, open conditions (CSTR) we may find multistability, hysteresis, extinction, ignition and anomalous relaxation times Allowing for the finite lifetime of the catalyst (B→inert products) adds another dimension The dependence of the stationary-states on residence-time now yields isolas or mushrooms Sustained oscillations (stable limit cycles) are also possible The onset of oscillation corresponds to a change in the character of the stationary-state (from stable focus to unstable focus) and the conditions for this change can be evaluated analytically The period of the oscillations and their amplitudes increase as the residence time is lengthened A total of nine different phase-portraits in the a–b plane has been found The isothermal system is less complex than the exothermic, first-order reaction in a CSTR, but there are strong analogies between the two

Heat transfer and kinetics in the low temperature pyrolysis of solids

Abstract: New theory is developed to define the parameters controlling the pyrolysis rate of single particles. It is shown that the relative importance of internal and external heat transfer and of the intrinsic (first order) pyrolysis kinetics can be determined from the Biot number (hR/K) and, depending on the value of the Biot number, one of two Pyrolysis numbers defined by Py = (K/kϱcpR2) or Py′= (h/kϱcpR). On the basis of these groups four regions are defined, and appropriate and simple models of the kinetics of primary pyrolysis outlined. The models are tested against measurements of decomposition and temperature distributions in pyrolysing wood cylinders with diameters in the range 0.6–2.2 cm and at temperatures from 380 to 500°C. Good agreement with theory is found and it is concluded that, under these conditions, internal convection is unimportant and that with suitably large or small values of Bi, Py and Py′ very simple models are adequate. Some implications for reactor design are briefly discussed.

Mathematical model of the thermal regeneration of a wall-flow monolith diesel particulate filter

Abstract: A wall-flow monolith filter placed in the exhaust stream of a diesel engine can effectively limit the emission of diesel particles through the monolith. The accumulated particles can then be periodically combusted inside the monolith by directing hot gas from a fuel burner to the monolith while the normal engine exhaust is routed around the burner/monolith system. The resulting low flow rates through the monolith require consideration of gas dynamics through the channels as well as particle combustion to analyze this regeneration process. A mathematical model of the regeneration is formulated as a system of nonlinear partial differential equations describing the conservation of mass, momentum and energy. Numerical solutions are obtained by using a combination of finite element and finite difference techniques for the spatial discretization and using an implicit ordinary differential equation solver for the resulting time integration. A detailed discussion of the solution for a sample regeneration is given.

Scaling relationships for fluidized beds

Abstract: The independent nondimensional parameters governing the dynamics of fluidized beds are found by nondimensionalizing the differential equations governin By proper adjustment of the length scales, the particle density, and the bed superficial velocity it is possible to obtain exact similitude between geo

A fully predictive criterion for the transition between particulate and aggregate fluidization

Abstract: A simple general model for the interaction between a particle and the fluid in a fluidized suspension, enables a hydrodynamic criterion for the onset of bubbling in fluidized beds to be formulated in a compact and fully predictive form Excellent agreement is found between the proposed criterion and experimental observations reported in the literature for liquid beds and gas fluidized systems operating under both ambient and elevated pressure condi

Flow distribution and pressure drop in plate heat exchangers—II Z-type arrangement

Abstract: An analytical study is made to calculate the axial velocity and pressure distributions in both the intake and exhaust conduits of plate heat exchangers, the flow distribution in the channels between the plates and the total pressure drop. The analysis shows that there is a general characteristic parameter ( m ) for all the plate heat exchangers, which determines the flow behaviour. When m 2 is positive, the channel flow rates will decrease in the direction of the intake stream. When m 2 is negative, the channel flow rates will increase in that direction. In any case, the flow distribution tends to be uniform for low values of m 2 ( ≤ 0.01). If m 2 is kept equal to zero, the flow distribution will be purely uniform. The sign of m 2 may be controlled by the area ratio of the intake and exhaust conduits respectively, its magnitude is affected by the shape and the number of plates. The results show that very low flow rates or even no fluid flow might occur in some of the channels for large positive or large negative values of m 2 . The analysis might be useful not only for the proper design of plate heat exchangers but also for many other technical systems with manifold flow distribution and collection problems.

Characteristics of fluidization at high pressure

Abstract: Experiments were conducted to investigate fluidization fundamentals at pressures up to 6485 kPa using nitrogen as the fluidizing gas. The particles under study were coal, char and Ballotini. Both a three-dimensional bed (10.16-cm-i.d.) and a two-dimensional bed (1.9x 10.16cm) were used in the experiments. The fundamentals of high pressure fluidization examined in this study include minimum fluidization velocity, bed voidage at minimum fluidization, bed expansion, and bubbling behavior. An empirical correlation was developed for determining minimum fluidization velocity. The effects of pressure upon bed voidage at minimum fluidization and expanded bed height were analyzed for several types of particles. High speed photographs were studied to describe bubbling behavior in a fluidized bed over a range of pressures.

Viscosity of Crude Oils

Abstract: A series of experimental viscosity data for seven different North Sea oils is presented. A new corresponding states method for prediction of the viscosity of both gaseous and liquid hydrocarbon fluids has been developed. The required input is critical constants and the molecular weight of each component. Very accurate results were obtained for the crude oils using the C 7+ -characterization procedure of Pedersen et al .[1]. The viscosity correlation is also shown to give satisfactory results for pure hydrocarbons and binary mixtures.

Lateral migration of spherical particles in porous flow channels: application to membrane filtration

Abstract: Lateral migration of spherical rigid neutrally buoyant particles moving in a laminar flow field in a porous channel is induced by an inertial lift force (tubular-pinch effect) and by a permeation drag force due to convection into the porous walls. The analysis of Cox and Brenner [7], for the particle motion in a nonporous duct is extended to include the effect of the wall porosity. Criteria are established under which the inertial and permeation drag force in the lateral direction can be vectorially added. Particle trajectories and concentrations profiles are calculated for a plane Poiseuille flow with one porous wall. For particles with radius of 1 μm, inertial and permeation drag forces are of comparable size under flow conditions often met in ultra- and hyperfiltration of dilute suspensions. For smaller particles the permeation drag force dominates.

Scaling relationship for fluidized beds

Abstract: Developpement systematique d'un ensemble de lois d'extrapolation qui peuvent etre utilisees pour concevoir un lit fluidise dans les conditions ambiantes. Ces lois d'extrapolation fournissent un ensemble de parametres sans dimension independants qui peuvent servir a caracteriser les regimes d'ecoulement et le comportement dynamique du fluide d'un lit fluidise quelconque

Global analysis of the multiplicity features of multi-reaction lumped-parameter systems

Abstract: Mathematical models of lumped-parameter systems in which many chemical reactions occur simultaneously contain a large number of parameters, so that a p Theoretical guidance is needed to determine all the multiplicity features and the corresponding parameter regions. A systematic, efficient scheme is presented for finding parameter values corresponding to a specific number of solutions. A new scheme is developed for bifurcation diagrams, which describe the dependence of a state variable on a slowly changing operating variable. Some general predictions are made abou systems. Bounds on the values of the bifurcation or state variable may create bifurcation diagrams which cannot be found close to the highest order sin of solutions even when an isola variety does not exist. Several examples illustrate the application of the mathematical techniques.

Affinity separations utilising immobilised monoclonal antibodies—a new tool for the biochemical engineer

Abstract: This review paper describes a new technique in biochemical engineering that is now being used for the purification of proteins for use as pharmaceuticals or in other applications where the purity of the product is an important consideration. The technique involves the immobilisation of antibodies to inert supports in order to form biospecific adsorbents that can be used in purification processes. The biospecific adsorbents that are formed have a high affinity for a single compound and are ideally suitable for the purification of proteins from a variety of biological sources. The main aim of the review is to introduce the biochemical principles on which the technique is based in order to lay the foundations for the adoption of the process in the near future as a new industrial unit operation. The review covers briefly the problems associated with the purification of proteins on a large scale and highlights the potential of affinity separations as industrial unit operations for this purpose. The reasons for using immobilised monoclonal antibodies are explained and advantages and disadvantages are discussed. The design of all stages of an affinity separation process is reviewed and a theoretical analysis of mass transfer in biospecific adsorption processes is presented. The performance of simple batch and fixed bed adsorption systems is compared and the suitability of their use in large scale separations is discussed together with techniques and procedures for the elution of the product and the regeneration of the adsorbent. Other aspects of the process design that are covered include the control of the repetitive operation of an affiinity separation process and the choice of support matrix and method of antibody coupling. Finally there is a brief consideration of other downstream processing stages likely to be necessary on both sides of the affinity separation process.

A replacement for the logarithmic mean

Abstract: A new mean has been developed as an approximation to the logarithmic mean. It may be viewed as a refinement of the arithmetic mean: the latter has been a useful approximation in economic analysis [5,6], whilst the new mean should find use both in flowsheeting programs and in rapid rating calculations a in the example above. The principal lesson is that the new mean is so tractable mathematically, and such good approximation to the logarithmic mean, th it merits serious consideration as a replacement for the logarithmic mean in many applications.

Flow distribution and pressure drop in plate hear exchangers. I. U-type arrangement

Abstract: Calcul de la vitesse axiale et de la distribution des pressions dans les conduites d'entree et de sortie de l'echangeur, de la distribution de l'ecoulement dans les canaux entre les plaques et de la perte de charge totale

Improvement of the Van Der Waals equation of state

Abstract: The Van Der Waals equation of state has been modified in order to improve its accuracy. The introduction of a temperature dependence of the attraction term allows reproducing accurately pure-compound vapour pressures. The modification of the mixing rules, with the infinite-pressure excess-free-energy term expressed by a NRTL-like model, allows reproducing accurately phase equilibria of polar and apolar systems. Finally, the introduction of a volume correction improves markedly the calculated liquid densities, without changing the phase-equilibrium conditions. The improved equation is accurate enough to be applied for design purposes.

The Adsorption of basic dye onto silica from aqueous solution-solid diffusion model

Abstract: The adsorption of Basic Blue 69 dye onto silica in a batch adsorption system has been studied A two resistance mass transfer model has been developed based on film resistance and homogeneous solid phase diffusion An analytical solution is presented and experimental results and theoretical data are in good agreement, for a wide range of operating conditions, using a single external mass transfer coefficient and a single effective solid diffusivity The variables investigated are: initial dye concentration, solid/liquid ratios and adsorbent particle size range Under constant agitation conditions almost all data can be correlated using a film mass transfer coefficient of 20 x 10−4 cm sec−1 and a diffusion coefficient of 12 x 10−9 cm2 sec−1

Fluidization of powders showing degrees of cohesiveness—I. Bed expansion

Abstract: The expansion characteristics of non-bubbling fluidized beds of powders having mean sizes from 125 to 3 μm have been measured. The ratio of the tapped bulk density to most loosely packed bulk density gives a good indication of the cohesivity of the powder and has been used in conjunction with the Richardson-Zaki equation to correlate the data.

Absorption of carbon dioxide into aqueous methyldiethanolamine

Abstract: Gas absorption rates in a laminar liquid jet were measured for carbon dioxide in methyl- diethanolamine (MDEA) solutions. It was found that for the short contact times (

Two-phase gas-liquid flow in rectangular channels

Abstract: The results of investigation of hydraulics in a two-phase gas—liquid flow in vertical and horizontal rectangular channels have been presented in the paper. Flow regime maps have been worked out and a method for calculating the pressure drop in a two-phase mixture flow has been proposed. The methods applied in a two-phase flow in pipes have been used to describe the results of investigations, after adopting the correction for the difference between the flow in rectangular channels and that in pipes.

Development of transport equations for multiphase system—I: General Development for two phase system

Abstract: The spatial averaging theorem is used to develop transport equations for the average concentration of a solute being distributed between two phases by convection, diffusion, and interfacial transport. Closure schemes are formulated for the spatial deviations in concentration by developing transport equations for these deviations. This formalism allows a priori predictions of the transport parameters. What results is a two-equation model, one equation for the average interstitial solute concentration in each phase. From a moment analysis of the resulting averaged equations, one can predict model behavior for long times in pulsed systems. It is found that the pulse velocities in each phase become equal and constant, and that the two equati model described here reduces to a single dispersion equation for sufficiently long times.

Kinetics and mechanisms of the reactions of carbon dioxide with alkanolamines: a discussion concerning the cases of MDEA and DEA

Abstract: A recent paper by Blauwhoff et al. (1984) has incited us to reexamine some of our previous results concerning the kinetics of reaction of CO2 with methyldiethanolamine (MDEA). The results can be very satisfactorily interpreted if an amine-catalyzed reaction with a rate constant 3.2 ( ± 1.0) M −1 s −1 is introduced in the theoretical simulations. This value agrees fairly well with the value obtained by the authors mentioned above (4.8 M −1 s −1. The influence of the pKA value of the amine on the theoretical simulation is also examined. The mechanism proposed by Blauwhoff et al. for the diethanolamine (DEA) reaction with CO2 is discussed and the values of their kinetic constants are compared with our value.

The determination of zeolite crystal diffusivity by gas chromatography—II. Experimental

Abstract: Experimental results are reported for the adsorption of propane and n -butane in a column packed with Linde 5A zeolite crystals, and methane, propan n - and iso -butane in a column packed with silicalite crystals The adsorption equilibrium constant K and crystal diffusivity D c , we obtained at different temperatures in the range 100–300°C, for each sorbate and packing and the heat of adsorption and diffusional activation energ were determined The results show that in order to separate the effects of K and the pressure drop, the latter must be independently estimated by a suitable correla

Experimental verification of scaling relationships for fluidized bed

Abstract: To verify the scaling relationships for fluidized beds, an atmospheric fluidized bed combustor and a cold bed constructed to operate at the same values

The enrichment of heavy water in a batch-type thermal diffusion column

Abstract: The separation equations for the enrichment of heavy water in a batch-type thermal diffusion column have been derived for low-concentration operations. The experimental works for various feed concentrations of H 2 OHDOD 2 O system has been also conducted and the results quantitatively confirm with the prediction of the theory.

Free radical polymerization engineering—I: A new method for modeling free radical homogeneous polymerization reactions

Abstract: This paper deals with a new appraisal of free radical polymerization modeling. Classical properties of the distribution of polymerization degrees and methods for studying them thanks to the z -transform are recalled. When simple mechanisms are involved, the kinetics may be represented by a “detailed analytic” model relying on macromolecule balances. This is no longer possible when complex processes are occurring, e.g. transfer to polymer, β-scission, terminal double bond propagation… In order to deal with these more complex cases, a “tendency model” is proposed, relying on balances of quantities such as free radicals, macromolecules and the moments of the distribution of polymerization degrees. The quality of the polymer is described by chemical characters such as double bonds, long and short branching points, terminal double bonds… for which kinetic equations are established. Equations are given for calculating the moments of free radicals and those of instantaneously produced macromolecules via various processes. The simplicity and the usefulness of the method are illustrated by several examples and a comparison is made, when possible, with the detailed approach. Finally, equations are given, making it possible to calculate the quality of polymer produced in any kind of reactor and for different states of segregation.

The diffusion coefficients of helium, hydrogen, oxygen and nitrogen in water determined from the permeability of a stagnant liquid layer in the quasi-s

Abstract: At temperatures between 10 and 60°C the diffusion coefficients of helium, hydrogen, oxygen and nitrogen in water have been determined from the permeability of a stagnant liquid layer in the quasi-steady state (SLL method). With this method we actually measure the difference in diffusive flow between two gases through a horizontal stagnant liquid layer between gas-permeable membranes. If oxygen is one of the gases, we are able to determine the diffusion coefficient of oxygen with a maximum experimental error of 3.5% and that of the other gases within 5%. Results are given and compared with experimental values stated in the literature.

Hydrodynamic behaviour of a draft tube gas-liquid-solid spouted bed

Abstract: Experiments were conducted using various types of solid particles to investigate the hydrodynamic properties of a gas-liquid-solid spouted bed with a draft tube. The hydrodynamic properties under study include flow modes, pressure profile and pressure drop, bubble penetration depth, overall gas holdup, apparent liquid circulation rate and bubble size distribution. Three flow modes were classified: a packed bed mode, a fluidized bed mode and a circulated bed mode. It was found that the friction factor accounting for the friction loss in the bed varies linearly on a logarithmic scale with the Reynolds number defined based on the apparent liquid circulation rate. The bubble penetration depth in the annular region, overall gas holdup and apparent liquid circulation rate increase with an increase in gas or liquid velocity. At high gas flow conditions an optimal solids loading exists which yields a maximum apparent liquid circulation rate. A model was proposed to describe the liquid circulation behaviour in the draft tube three-phas spouted bed. The average bubble size in the draft tube region is higher than that in the annular region for both the dispersed bubble regime and the coalesced bubble regime in the draft tube region.

Sequential experimental design for model discrimination in the case of multiple responses

Abstract: The sequential experimental design procedure for discriminating among single response rival models outlined in Chem. Engng Sci 1983 38, 225 is here extended to the case of multiresponse models. The method is illustrated with an example.

Mass transfer to large particles in fluidised beds of smaller particles

Abstract: A theory is proposed for predicting the transfer of a gas through a fluidised bed of small particles to a large particle. It is proposed that non steady-state mass transfer of the gas occurs by two mechanisms: (i) mass transfer of gas in clusters or packets of the smaller particles approaching the large particle; and (ii) gas convection. The theory developed enables prediction of the Sherwood number (Nsh, the dimensionless mass transfer coefficient) for a large particle, diameter d: Nsh=2emf+4g3mfd(Umfemf+uinb)/π DA12 where Umf is the minimum fluidising velocity, emf is the bed voidage at Umf-0ub is the mean bubble rise velocity and DA is the gas diffusivity. This equation is shown to be in excellent agreement with Sherwood numbers determined from combustion experiments in which single large particles of petroleum coke were burned in air fluidised beds over a wide range of operating conditions. It is also shown that predictions using this expression are in close agreement with those from an empirical expression previously proposed by the autho

The dynamic behaviour of continuous polymerization reactors—III: An experimental study of multiple steady states in solution polymerization

Abstract: A study involving small scale reactor experiments coupled with detailed non-isothermal reactor modelling has been carried out shows that ‘isoia” ty