THE “UCKRON-1” TEST PROBLEM FOR REACTION ENGINEERING MODELING

Testing kinetic models against a “true” and detailed kinetic expression was the aim of the Workshop on Kinetic Model Development at the Denver AIChE Meeting in August, 1983. For this purpose an artificial reaction mechanism was created, based on the known thermodynamics of the methanol synthesis as a framework. The kinetic rate laws, that were derived from this mechanism, were made thermodynamically consistent by achieving agreement between equilibrium constants calculated at various temperatures from the given, real original thermodynamic relationship and those calculated from the detailed reversible kinetic expressions.

Using the artificial kinetics as the "true" one, CSTR experiments were simulated. The results of a statistically designed set of experiments were published after 5% random error was added to the data. Participation was invited for all interested to correlate the data, develop kinetic models and to calculate the performance of the specified reactor.

The results of 19 submitted entries are summarized with the conclusion that the models had more differences than were expected, but their predictive values were not as different as was anticipated, if the extreme high production rates due to thermal runaways are not considered. This in turn points out the necessity to check models experimentally, in pilot plant, not only for predicted optimum, but also for calculated runaway conditions. Models which did not capture the true character of this reaction failed to predict the onset of runaway reactions.     

UCKRON II TEST PROBLEM THE EFFECTS OF PORE DIFFUSION

The UCKRON I test problem was reworked with the inclusion of diffusional limitations to the kinetics. For this purpose, the rate expressions, i.e. the full kinetic model and the Langmuir-Hinshelwood model, proposed in the previous workshop, were assumed to represent the true kinetics.

A simple mathematical model based on simplified effective diffusivities and the “Dusty-Gas” model were used to take account of pore diffusion resistance within the catalyst particle. These models predicted effectiveness factors based on the reaction at the bulk conditions. The effectiveness factors were then correlated against temperature and the partial pressure of reacting species.

These correlations were then used to predict the temperature profiles within the water cooled plug flow reactor for various values of cooling media temperature.     

THE EFFECT OF NON-IDEALITY OF REACTING MIXTURE ON SIMULATING THE METHANOL REACTOR

In modeling the methanol reactor, specified for the 1st International Workshop on Kinetic Model Development (Berty et al. [1]), the Soave-Redlich-Kwong equation of state was used to describe the non-ideality of reacting mixture and to calculate fugacity and enthalpy. The temperature profile, production rate, “runaway” condition and the equilibrium conversion calculated from non-ideal gas law were compared with the calculations assuming ideal gas behaviour. The kinetic equation choosen was the artificial one proposed by Berty et al. [1].     

A NONLINEAR OBSERVER BASED ON HYBRID MODELLING OF CHEMICAL REACTORS

The successful design of an observer for inferring the outlet composition from a chemical reactor heavily relies on the goodness of the adopted kinetic rate model (Baratti et al., 1993). On the other hand, often, it is difficult to dispose of a simple, but, exhaustive kinetic model because of the complexity of the reaction scheme one has to deal with.

In this work, we explore the possibility to represent global (lumped) reaction rate laws by the use of neural network models. The aim is to develop a nonlinear observer (extended Kalman filter, EKF) of an heterogeneous gas-solid reactor that relies on a grey model where the “neural reaction rate” law is integrated within a first principles model. The procedure is outlined for the case of the catalytic oxidation of carbon monoxide over Pt-alumina catalyst. The results show that neural networks (NN) can be effectively used in representing lumped reaction rates since NN are able to capture the essential characteristics of the functional relationship relating the state variables.     

Interfacial Contact and Bonding in Autohesion V—Bonding of “Flat” Surfaces

All surfaces, when viewed under the microscope, are found to be rough. When the so-called “flat” surfaces are bonded together, the initial contact is only at the high points in the surface. This contact increases with time and the rate of contact establishment is a function of surface roughness and the viscoelastic properties of the material.

A surface study of the “flat” compression-molded surface is made. The profiles are generated by tracing the surface with a stylus. The Interference Microscope is used to study the region in the vicinity of an asperity.

The surfaces are approximated to be composed of simple spherical segments. The deformation is conceived of as a two-stage process. The first stage of easy deformation controls the initial bond strength. The initial bond strength predicted by theory agrees well with experiment.     

ESTIMATION OF FUNCTIONS IN DRYING EQUATIONS

In drying problem, particularly for drying foodstuff, modelling is very difficult. Many physical effects have to be taken into account for mass transfer ; then mass transfer coefficient varies

In different models unknown functions must be estimated. It is particularly the case in simple models of drying using average values of water content, where the mass transfer varies versus mean water content in falling rate period. On the other hand in the “diffusion model” we have the same problem concerning the diffusion coefficient which must be also estimated

The method we propose in this paper for these two models : simple and “diffusion model” of drying consists from measurements of temperature and water content of the product to search a numerical approach of the unknown function. This method uses optimization techniques on computer and least squares criterion between model values and experimental data

Results are given for the “diffusion model” applied to shelled corn drying to find the diffusion coefficient and for a simple 11107 del applied to plum drying to find the mass transfer coefficient.     

COMPUTER SIMULATION OF HYDRODEMETALLATION IN FIXED-BED REACTORS

An isothermal model for hydrodemetallation (HDM) of crude oils in catalytic fixed-bed reactors is proposed. This model involves a consecutive reaction mechanism, which is capable of accounting for particle deposit profiles with interior maxima. Consistent with the fact that HDM catalysts are conglomerates formed by precipitation, the porous catalyst itself is modeled as randomly overlapping spheres of equal size. The metal is deposited as growing metal sulfide crystallites on the inner surface of the catalyst. These crystallites originate from a certain number of randomly scattered nuclei and increase in size as the deposition proceeds. The random sphere model for the catalyst and the deposit provides the changes in the catalyst pore structure—local porosity and surface area.

The mass transport within the domain of the particle is due to restricted liquid diffusion, since the diameter of the metal bearing compound (porphyrin) and the intermediate are comparable to the pore size. The diffusion restrictions taken into account are the enhanced drag imposed on a molecule by adjacent pore walls and steric partitioning.

Since the deposition process is much slower than diffusion and reaction, the pseudo-steady-state assumption can be justified. The equations of conservation for mass are solved by orthogonal collocation on finite elements. Based on this solution technique a computer simulation program of HDM is designed that allows two modes of operation: constant temperature and constant conversion. The simulation program “SIMULA” is highly flexible with regard to reaction kinetics, catalyst structure, reactor design, and operating conditions. In comparison to a base case with uniform activity, the effect of intraparticle (radial) and bed (axial) activity profiles on the conversion rate is discussed. For the case investigated, a radial distribution of activity higher at the center of the particle than at the edge can increase catalyst life by 25%, but axial distribution was less successful.     

ON CHARACTERIZATION AND MITIGATION O F COMBUSTION HAZARDS INVOLVED IN THE HANDLING OF PARTICULATE MATERIALS: A REVIEW OF THREE BOOKS

The three publications reviewed herein deal with the complex of hazards which may derive from the agricultural and commercial handling of combustible particulate and gaseous materials. The principal thrusts of each book differ substantially from those of the other two. This review first attempts to consider the essential combustion processes which underlie the hazards of common concern in all three works. Each of the three books is then considered on an individual basis. The three publications are designated Books (1)- (3) respectively and are listed below:

(1) “User Guide to Fire and Explosion Hazards in the Drying of Particulate Materials.” 1977. Institution of Chemical Engineers. Warwick Printing Company Limited, England.

(2) “Prevention of Grain Elevator and Mill Explosions.” 1982. NAS-NRC Publication NUB 367-2. National Academy Press, Washington, D. C.

(3) “Guidelines for the Investigation of Grain Dust Explosions.” 1983. NAS-NRC Publication NMAB 367-4, National Academy Press, Washington, D. C.     

ISOTHERMAL AND NON-ISOTHERMAL MULTICOMPONENT ADSORPTION KINETICS

The model equations in the relaxation form for the multicomponent kinetics of isothermal and non-isothermal adsorption, taking into account all major distinctive features of the interphase heat and mass exchange inside porous grains and at their surface (see points 1 to 4 below) for P (“pore”) and S (“solid”) models of mass transfer within porous grains of the adsorbent, have been obtained.

First for isothermal and non-isothermal kinetics in the mixed kinetics region of mass and heat exchange in the absence natural mutual diffusion and natural thermal-diffusion the essential influence effective mutual diffusion and effective thermal-diffusion is shown.

Recommendations on the use of model equations of adsorption kinetics for describing isothermal and non-isothermal adsorption dynamics of multicomponent mixtures in the inner-diffusion and mixed (outer- and inner-diffusion) kinetic region of heat and mass exchange are made.     

“GENERALIZED” ENTROPY PRODUCTION RATE ASSOCIATED TO ONE-DIMENSIONAL HEAT CONDUCTION- EXTREMUM POINTS AND APPLICATIONS

In previous papers, the author considered the critical or the extremum points of the entropy production rate in insulations with one-dimensional heat conduction, either alone or associated with other refrigerating systems necessary to maintain the steady state.

The aim of this paper is to obtain a general formulation for the presence of critical or extremum points of the (generalized) entropy production rate in a more ample domain that includes the previous cases as particular ones.

Homogeneous and more than one component systems are considered; for homogeneous systems, the necessary and sufficient condition for the minimum of the (generalized) entropy production rate in the system is obtained, while for two or more component systems only the necessary condition for a relative extremum is stated. In the latter case one can have also a particular state which is not an extremum and can be known as a “saddle point” state from analogy.

This general formulation can be used for the thermodynamic optimization of cryogenic plants, extensively used in large-scale superconducting plants operating at liquid helium temperatures.     

Book Reviews

“lssledovaniya v oblasti poverkhnostnykh sil” (“Research on surface forces”) B. V. Deryagin, editor. Nauka Publ., Moscow 1967.544 pp. Rubles 3.00.

G. D. Andreevskaya, “Vysokoprochnye Orientirovannye Steklo-plastiki” (“High-strength Oriented Glass-Plastics”). Nauka Publ., Moscow 1966. 370 pp., Rubles 2.12.

A. D. Zimon, “Adgeziya pyli i poroshkov” (“Adhesion of dust and powders”) Khimiya Publ., Moscow 1967.372 pp. Rubles. 1.51.

J. J. Bikerman, “The Science of Adhesive Joints”. Academic Press, New York 1968.349 pages. $16.00.     

NUMERICAL SIMULATION OF TURBULENT FLOW OF AGITATED LIQUID WITH PITCHED BLADE IMPELLER

The turbulent flow field in an agitated system with baffles was solved numerically using the standard k-e model, an algebraic Reynolds stress model (ASM) and a differential Reynolds stress model (RSM). The commercial software FLOW3D (CFDS, Harwell Laboratories, 1991) was used for this purpose. The aim of the study was to investigate the influence of the impeller boundary conditions and turbulence models to the agreement with experimentally obtained laser-Doppler anemometry data. The boundary conditions for the impeller discharge used in the numerical calculations were obtained as whole-cycle-ensemble averages from experimental LDA-measurements (Fort et al., 1992). Since measurements of the rate of dissipation of turbulent kinetic energy ( ε) was not available the dissipation rate per unit mass in the impeller discharge was estimated from the expression:

where k is the turbulent kinetic energy per unit mass and L the macroscale of turbulence in the pitched blade impeller discharge. The macroscale of turbulence (L) in the impeller boundary condition for e was varied in order to optimize the fit of theoretically obtained profiles of turbulent kinetic energy with experimental data. The constant A was fixed to 0.85 according to Wu and Patterson (1989). The optimal values of L for the different turbulence models were compared with the projected height of the impeller blade (h). All three components of the mean velocity were compared with experimental data for the optimal ratio of L/h for six radial cross-sections in the tank.

The mean velocity field obtained from simulations showed good agreement with experimental data for all models, with somewhat better agreement for the k — e model. An optimal value of the ratio L/h was found to be equal to 2.0 for the k — ε model and 1.3 for the ASM. However, no such optimal value for the RSM could be determined in this study.     

ABSORPTION AND DESORPTION TO AND FROM LIQUID FILMS ON INCLINED PLANES

Two published theoretical models are examined and applied to experimental results for absorption and desorption. The system used was CO₂/H₂O and studies were made for liquid film flow down inclined planes. Experimental results give “Reduced” values of mass ransfer rates.

Interferometric studies give interfacial concentration, penetration and film depths, and take-up of carbon dioxide. In the case of desorption the interferograms are distorted by “deflections.”

All the experimental values for absorption and desorption differ from those calculated from theoretical models.

Desorption is not a mirror image of absorption, and it is approximately 75% of the transfer rate of absorption over a wide operating range.

A comparison is made of the behaviour of static pools and flowing liquid films.     

MULTIPLE STEADY STATES IN NON-ISOTHERMAL FT SLURRY REACTOR

A model for a non-isothermal, semi-balch (stagnant slurry and flowing gas), laboratory scale Fischer-Tropsch (FT) slurry reactor is developed. The model assumes the existence of FT and water-gas shift (WGS) reactions. The reactor configuration is assumed to be the same as one used by Bhattacharjee et at. (1986). Gas-slurry mass transfer coefficients, solubility parameters and other physical transport and kinetic parameters used in the model are obtained from the reported studies of Lieb and Kuo (1984), Bhattacharjee et al. (1986), Deckwer et al. (1982, 1986) and Karandikar et al. (1987( for the FT slurry system

The model is used to evaluate the relevant kinetic constants and the heat generation parameters for the FT reaction from the experimental data of Bhattacharjee et al. (1986). The nature of the heat generation curves indicates that multiple steady states are likely to occur in a non-isothermal FT slurry reactor. The ignition temperatures are calculated as functions of gas hourly space velocity, activation energy for the FT reaction, reactor pressure, and coolant temperature and flow rate. In general, these temperatures are in good agreement with those reported by Bhattacharjee et al. (1986). The exact values of the ignition temperature are strongly affected by the magnitudes of the activation energy and the heat of FT reaction. Once the reactor is ignited, the catalyst changes its character leading to the multiple branches of heat generation and product distribution curves. The extinction temperature was, therefore, not observed in Bhattacharjee's experiments.     

RECIRCULATING REACTOR FOR THE STUDY OF MULTIPHASE KINETICS

A new laboratory reactor was set up to measure kinetic coefficients in a solid (catalyst)-liquid-gas reacting system.

The reactor consists of two parts: an absorber, where the liquid is partially saturated by the gas reactant and a reacting zone, where the liquid alone, containing the dissolved gas, flows through a fixed bed of catalyst.

The ricircle of the liquid in the absorber maintains a high concentration of the gas reactant in the liquid also in the zone of reaction, allowing the use of a high mass of catalyst (significative from a statistical point of view) and the achievement of sufficiently high conversion.

The tested reaction is the catalysed hydrogenation of ∝-metylstyrene: in order to consider a drastic situation and to verify the results with the literature data, the experimental conditions examined corresponded to very high chemical reaction rate (instantaneous reaction) at the surface of the pellets.

The tests were carried out with the reactor working both in batchwise and in continuous operative mode (steady state); the results show the reliability of the new reactor above all when the steady state operation is considered. For the use of the reactor in batchwise condition, the accumulation of the product inside the catalyst particles must be considered for an accurate measurement of the kinetic parameters,     

Adhesion of Plasticized Polyvinyl Butyral) to Glass

A study of safety glass provides a good example of the interplay among the many physical properties involved in “adhesion”, and the relationship between adhesion and performance. This work demonstrates the value of applying known fundamentals to practical problems.

An idealized model of a windshield fracture event is described in terms of interactions among mechanical responses of the interlayer, the fracture characteristics of the glass and the high speed, low angle peel behavior.

Data on the surface energies of glass, polyvinyl butyral) and water show that at thermodynamic equilibrium a stable system comprising glass, water and polyvinyl butyral) phases, an aqueous phase must lie between the glass and PVB.

The potassium salts are shown to be effective because they are deliquescent and give solutions at equilibrium with the water in the PVB at water contents of ∼0.40% or higher. The greater the amount of salt at the interface and the higher the water content of the sheeting during lamination, the thicker the interfacial layer and delamination occurs more readily. This relationship is quantified using a modified form of the Stefan equation.

Data on diffusion of water and salt are shown to be consistent with the amount of salt at the interface required for the observed performance (∼ 3 mg KAc/m²).

Data on electrical resistivity of the interface correlate with peel force and provide convincing support for the hypothesis.     

SUBLIMATION OF PURE SUBSTANCES IN GAS FLUIDIZED BEDS AT ATMOSHPERIC PRESSURE.

This paper deals with the sublimation of large bodies, or “objects”, made up from a pure substance in a bubbling gas fluidized bed of considerably smaller particles, or “fines”. The influence of such parameters as the gas velocity, the bed temperature, the size and the adsorption capacity of the fines has been investigated.

The results obtained clearly show that the rate of sublimation in fluidized beds is far higher than in air alone. It increases with increasing bed temperature, decreasing particle size, increasing powder mass capacity, and roughly varies as a parabolic function of time. It has also been observed that the temperature difference between the bed and the object surface, or “temperature depression”, depends on the fines characteristics as well as on bed temperature, but is independent of gas velocity when good solid mixing conditions are achieved.

Bed-to-object heat and mass transfer coefficients have been deduced from data points and attempts have been made to provide a reasonable theory to account for them. After a complete examination, the idea of interpreting transport phenomena based on a well-adapted “surface renewal model” has been proposed.     

The Influence of Structure on Autohesion (Self-Tack) and other forms of Diffusion into Polymers

Autohesion is discussed emphasising in particular the influence of polymer chain structure on apparent rates of diffusion. The full range of autohesive levels which exists amongst rubbery polymers is rationalised by proposing a distinction between inter-chain free volume and “intra-chain” free volume, the latter being a collation of free volume regions “contained” in cavities associated with permanent polymer chain structural features which especially apply for certain polymer types. The coincidence of several such cavities plus the intervening inter-chain space causes the formation of holes which may attain sufficient size during normal chain thermal fluctuations to facilitate forward motion of an incoming chain.

The concept of free volume has been used to demonstrate the proposed model semi-quantitatively. Comparison with a simple model, involving inter-chain free volume only, is made throughout the calculation. The proposed model, in showing general agreement for several elastomers between free volume considerations and autohesive characteristics, provides an explanation for the large difference in tackiness which exists between natural rubber and ethylene propylene copolymers.

The relationship of the proposed model with chain co-operative motion is discussed, and its apparent correlation with the diffusion through polymers of a range of gases and solvents is discussed in some detail.     

DEVELOPMENT OF RADIAL MODELS FOR FORMATION DAMAGE IN POROUS MEDIA

The continuously changing velocities in radial geometry have a significant effect on process characteristics, making it an intellectually challenging problem. In practical operations, fluid is generally pumped down injection wells from where it flows radially outward. Simulating this radial system with linear models is definitely restrictive. Consequently, the need for developing radial models for flow and particle entrapment in porous media is both fundamental and applied.

A radial network model, covering a 120° angle, has been developed to simulate formation damage due to deep bed filtration (DBF) of injected suspensions. The models draws upon our previously developed concepts of “wave-front movement” and “flow-biased probability” for linear systems. Systematic studies have been performed on formation damage using monodispersed and polydispersed suspensions. Case studies have been presented for constant flow rate and constant pressure injections, and comparisons are made between linear and radial systems.

Results show that the results obtained from linear models are conservative in comparison to those obtained from radial models. Furthermore, the use of monodispersed particles in mathematical models would show smaller differences between linear and radial predictions than would actually occur for polydispersed particles.