AN EMPIRICAL VIRIAL-LIKE CUBIC EQUATION OF STATE FOR PHASE EQUILIBRIUM CALCULATIONS

An empirical cubic equation of state(EOS) was obtained by truncating the virial expansion in reciprocal of molar volume after the third term. The constants of the EOS was generalized in terms of critical temperature, critical pressure and Pitzer's acentric factor.

In pure component applications the EOS exhibited a performance comparable to Peng-Robinson (1976) EOS in the reduced temperature range of 0.5 to 1. The present EOS tends to predict better saturation liquid volumes at reduced temperatures below 0.8, and better estimations for second virial coefficient at high reduced temperatures.

The EOS was successfully employed for vapor liquid equilibrium calculations for some mixtures of normal or slightly polar fluids with traditional one binary parameter mixing rule at moderately high pressures. At low reduced temperatures, where conventional one adjustable parameter applications of the cubic equations compare unfavorably with dual methods based on excess Gibbs energy functions for the liquid phase, a new two constant mixing rule introduced by Stryjek and Vera (1986) was employed for the present equation of state.     

A MODIFIED LEE-KESLER EQUATION OF STATE FOR REFRIGERANTS

For calculation of the thermodynamic properties of refrigerants it is proposed that the extended corresponding states principle (ECSP) should be used using two specific reference fluids, CFC12 (CCI₂F₂) and HFC134a (CF₃CH₂F), in order to cover the field of interest for most refrigerants. The specific parameters of these refrigerants have been determined for the Lee-Kesler modification of the Benedict-Webb-Rubin equation of state. In the parameter estimation, it has been taken into accounl that all variables are subject to errors by using the so-called Error-in-Variables-Model (EVM). The parameters have been estimated from experimental pressure-volume-temperature data, vapour pressure and saturated liquid and vapour volume data for CFC12 and HFC134a.

The extended corresponding states principle proposed in this work with CFC12 and HFC134a as reference fluids has been used in calculations of the thermodynamic properties of a number of refrigerants. In comparison with the original Lee-Kesler equation this concept gives improved results in calculations of vapour pressure and liquid volume.     

UNSTEADY, TWO-DIMENSIONAL HEAT AND MASS TRANSFER IN A PACKED BED OF FINE PARTICLES WITH AN ENDOTHERMIC PROCESS

The basic differential equations controlling the temperature and concentration field in a single packed bed of fine particles were derived and solved for the general case in which unsteady, two-dimensional heat and mass transfer lakes place with an endothermic process.

The time-change of particle- and fluid-temperature and concentration of water vapor (humidity) were calculated by a numerical method which assumed that the rate of the endothermic process can be expressed by a first-order rate equation and that the fluid flowing through the bed is of the piston flow type.

The experiments were conducted for the drying of silica-gel and the two-stage dehydration reaction of natural gypsum to demonstrate the applicability of the present theoretical analysis.

It has been found that the calculated results show satisfactory agreement with the measured data within the range of the experimental conditions employed.     

DYNAMICS OF FRACTIONATORS WITH STRUCTURED PACKING

A generalized dynamic mode! of a distributed staged (packed) fractionator is developed in this work. In particular we consider the dynamics of fractionators which employ structured packings as a means of achieving mass and heat transfer in multi-component systems.

The mathematical model is described by a large set of partial and ordinary differential equations coupled with non-linear algebraic constraints (PODAEs). These equations arise from the mass and energy balances on a distributed column-section together with the fluid dynamic relations. A computational algorithm is developed which employs a polynomial approximation leading to a large differential-algebraic equation (DAE) system. This is solved using standard implicit DAE algorithms.

In this work, the liquid holdup and transfer coefficients (both mass and heat) are computed from established correlations and detailed thermodynamic relations. This differs from most of the previous work reported, which used very simple correlations based on a single variable such as liquid or vapour rate. The results show that the more rigorous computation of transfer coefficients is essential to the veracity of the model.

The model has been applied to the case of an industrial depropanizer which uses a Mellapak 250Y structured packing. The generalized model can be used to study the control and optimization of such fractionators, which are becoming more prolific in the petroleum and related industries.     

THERMODYNAMIC PROPERTIES OF BINARY LIQUID MIXTURES OF ETHANE AND ETHYLENE WITH METHANE AND THE RARE GASES

Two series of binary liquid mixtures containing either ethylene or ethane have been investigated, at one or more temperatures (usually at the triple-point temperature of the component with the higher melting-point). In the ethylene series liquid-vapour equilibrium and liquid density studies were carried out for mixtures with methane, krypton and xenon; the heats of mixing were also measured for the ethylene + krypton mixtures. In the ethane series, which comprised mixtures with methane, argon, krypton and xenon, all three properties were measured except for the ethane + methane and ethane + argon systems where the enthalpies of mixing were already known. The ethylene + ethane system was also investigated at 161.39 K.

The results have been used to estimate the thermodynamic excess functions G^E, V^E and H^E. The G^E values decrease, within each series, as one moves from the lighter to the heavier rare gas, the values being lower in the ethane series. For the ethane + xenon mixtures both G^E and H^E are negative, showing a weak attraction between the two molecules. The V^E values for the mixtures of hydrocarbons suggest the probable formation of interlocking structures between the two components.

The values of the thermodynamic excess functions have been interpreted in the light of the model of Frisch-Longuet Higgins-Widom for the liquid state.     

EVALUATION OF THE ORIGINAL AND THE MODIFIED LEE-KESLER EQUATION OF STATE

In this work, the Lee-Kesler equation of state has been used together with the extended corresponding states principle. In order to improve the predictability of the equation in a more narrow acentric factor range, two new reference fluids have been chosen. The parameters in the Lee-Kesler equation have been estimated for the two reference fluids, CFC12 (dichlorodifluoromethane) and HFC134a (1,1,1,2-tetrafluoroethane), with the Error-in-Variables Model. This model allows both dependent and independent variables to be subject to errors.

Calculations have been made for the two reference fluids as well as for other compounds, and the predicted thermodynamic properties have been compared with experimental values. Comparative calculations have also been carried out for some of the previously suggested modifications of the Lee-Kesler correlation.     

KINETICS OF THE HYDROLYSIS OF ACRYLONITRILE TO ACRYLAMIDE OVER RANEY COPPER

Measurements of the kinetics of the hydrolysis of acrylonitrileover Raney copper catalysts have been made in the temperature range 40 to 100°C in a tubular reactor operated differentially with and without recycle and over concentration ranges of 0-25 weight percent acrylonitrile, 0-35 weight percent acrylamide and 40-99 weight percent water.

For the concentration range 0 to 7 wt. % acrylonitrile and 0 to 7 wt. % acrylamide, data were fitted by an adsorption model of the type

A + K,CA + KCCC and at higher concentrations by the powers law expression

The activation energy for the reaction was found to be 49.2kJmol^-1. Both models showed that the product acrylamide strongly inhibits the reaction.     

SCALE-UP OF CONTACT DRYERS

The scale-up of contact dryers is still based on experimental drying curves. In order to keep the effort to a minimum the drying curve is determined using a small laboratory or pilot dryer of similar geometry to the production dryer.

This paper introduces a new scale -up method for contact dryers. The new scale-up method is based on the assumption that heat transfer is the controlling mechanism. The scale-up method is derived from the material balance, the energy balance, the kinetic equation of heat transfer and thermodynamic equilibrium. The scale up method can be used to convert the drying time required to achieve a certain residual moisture content from the laboratory or pilot dryer to the production dryer and/or different drying conditions.

The scale-up method was verified by drying test with four different products in conical mixer dryers of 1, 60, 250, 1000 I volume. Two products were free flowing and two products were non free flowing in the wet state. The products can be considered non-hygroscopic in the moisture range investigated.     

KINETIC STUDY OF THE C3 CUT TAIL END SELECTIVE HYDROGENATION

In this paper, the kinetics of the tail end selective hydrogenation of a C₃ cut over palladized alumina catalyst have been studied. In the absence of finite transport limitations, experiments have been carried out to analyse the influence of methylacetylene ( and propadiene (PD) content in the feed, hydrogen/MAPD molar ratio, temperature and space time on the corresponding conversion and selectivity. The main aim of this process is to improve propylene yield by removing MAPD in the propylene rich cut.

The experiments were performed in an integral plug flow and the integral method was used for the kinetic analysis. The minimization of the objective function was made by the Marquardt algorithm for multiple response and the continuity equation set integrated by fourth order Runge-Kutta technique.

The most adequate models were the power law type for the experimental range. The comparison between experimental and observed values of the MAPD, propylene and propane molar fraction in the hydrocarbon mixture, which were used for the minimization, confirm the suitability of the fit.     

A DISTRIBUTED PARAMETER APPROACH TO THE DYNAMICS OF ROTARY DRYING PROCESSES

A nonequilibrium distributed parameter model for rotary drying and cooling processes described by a set of partial differitial equations with nonlinear algebraic constraints is developed in this work. These equations arise from the multi-phase heat and mass balances on a typical rotary dryer. A computational algorithm is devekped by employing a polynonial approximation ( orthogonal collocation) with a glotal splinc technique leading to a differential-algebraic equation ( DAE) system. The numerical solution is carried out by using a standard DAE solver.

The two- phase-flow heat transfer coelficient is computed by introducing a correction factor to the commonly accepted correlations. Since interaction between the falling particles are considered in the correction factor,the results are more reliable than those computed by assuming that heat transfer between a single falling particle and the drying air is unaffected by other particles. The heat transfer computations can be further justified via a study on the analogies between heat and mass transfer.

The general model devloped in this work is mathematically more ritorous yet more flexible that the lumped parameter models established by one of the authors (Douglas et al., (1993)). The three major assumptions of an equilibrium operation, perfect mixing and constant drying raic, are removed in the distributed parameter model.

The simulation results are compared with the operational data from an industrial sugar dryer and predictions from earlier models. The model and algorithm successfully predict the steady state behaviour of rotary dryers and collers. The generalized model can be applied to fertilizer drying processes in which the assumption of constant drying rate is no longer valid and the existing dynamic models are not applicable.     

EXPERIMENTAL STUDY OF THE SELECTIVE HYDROGENATION OF STEAM CRACKING C2CUT. FRONT END AND TAIL END VARIANTS

Selective hydrogenation is the habitual industrial process to eliminate the most unsaturated hydrocarbons, which are harmful for later applications. In this paper, the kinetics of the selective hydrogenation of a C₂ mixture over two palladium/alumina catalysts with both front end and tail end variants, have been studied. Experiments have been carried out to analyse the influence of temperature, hydrogen/acetylene molar ratio, carbon monoxide content in the feed and hydrocarbon volumetric flow rate on the corresponding conversion and selectivity.

The experiments were performed in an integral plug flow reactor and the integral method was used for the kinetic analysis. The minimization of the objective function was made by the Marquardt algorithm for multiple response and the continuity equation set integrated by fourth order Runge-Kutta technique.

The most adequate models were the power law type for the experimental range. The comparison between experimental and observed values of the acetylene and ethane molar fraction in the hydrocarbon mixture, which are used for minimization, confirm the suitability of the fit.     

VISCOSITY OF BIOMATERIALS

Viscosity data for honey, corn oil, mayonnaise, yogourt, blood and banana puree have been analyzed using two Theological models: the Herschel-Bulkley model and a proposed model. The proposed model contains three parameters: a yield stress, a parameter having the units of time and a parameter having the units of viscosity.

The model parameters were obtained by non-linear regression and the proposed model was shown to compare favorably with the Herschel-Bulkley equation.

An Arrhenius-type of correlation could be verified between the viscosity of banana puree and the inverse of the temperature. Also, the time parameter (t₁) of the proposed model could be correlated with the temperature and the parameter η₁.

It is asserted that the proposed model should replace advantageously the commonly used Casson expression.     

THE FLOODING CAPACITY OF PERFORATED PLATES IN ROTATING LIQUID-LIQUID-SYSTEMS†

Centrifugal extractors found wide applications in the industry, but up to now very little is known about what happens inside and how to calculate fluid-dynamic and mass transfer. For the basic research of dispersed liquid-liquid-systems in centrifugal fields a model centrifuge was built which is resistant to the high loads produced by rotation and which enabled us to observe the flow mechanism at the flooding points.

The processes inside have been measured and photographed by a high-speed-camera.

The calculation of centrifugal extractors is based mainly on the contact surfaces of the phases and the contact times. The maximum flow or flooding capacity is determined by three limits. Two of them are determined by the interface locations inside, controlled from the back pressure. The third limit is given by the maximum combined flow. This limit is dependent on the set of internals, the rotor speed and the physical properties of the liquid system. The experimental results will be shown and compared with new theories for the flooding capacities of perforated cylindrical plates in rotating liquid-liquid-systems.

The results predicted using the mathematical model for calculating the capacities are in fair agreement with the measurements.     

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,     

SEPARATION OF ETHYLBENZENE-XYLENES MIXTURES BY DISTILLATION: A POSSIBLE APPLICATION OF VAPOUR RECOMPRESSION CONCEPT

The application of direct vapour recompression to an existing plant, fractionating ethylbenzene-xylenes mixtures, has been studied.

The behaviour of the saturated liquid and vapour curves for ethylbenzene in the Temperature-Entropy diagram has been evaluated theoretically by means of well known equations of state. The most important operating parameters of the process (as functions of ΔT) in the reboiler-condenser have been obtained. The economic analysis performed indicates that for the case considered, the best value for ΔTis about 6°C, but only a small energy saving can be achieved.     

DEVELOPMENT AND VALIDATION OF A PROCESS SIMULATOR FOR DRYING SUBBITUMINOUS COAL

Drying subbituminous coal has never been practiced commercially. The commercial dryers built to date have been designed for drying surface moisture in conjunction with upstream coal preparation facilities. This type of drying is mainly controlled by input energy and the basis of the design is an energy balance. In drying inherent moisture from subbituminous coal, the thermal conductivity of the coal and the diffusion of molecular water within coal particles impose limitations on the process conditions. Energy input and solids residence time in the dryer have to be controlled properly for simultaneously balancing the heat and mass transfer within the coal particles. Improper control of either parameter can cause fires and explosions during the key steps of the drying process—drying and cooling

In parallel to the Anaconda coal drying pilot plant program, a cross-flow, fluid-bed coal drying/cooling process simulator was developed for: (1) understanding the drying phenomena on an individual particle basis; (2) analyzing potential risks and safety limits, and (3) designing the Anaconda pilot plant program

The development of the process simulator was based on both first principles and laboratory data and can be divided into two phases:

1 Development of a semi-mechanistic drying model for Powder River Basin subbituminous coal employing an analytical solution of the diffusion equation

2.Formulation of a fluid-bed cross-bed cross-flow dryer/cooler simulator employing simultaneous heat and mass transfer

This model was validated against process variables data taken on a 4 tph pilot plant. An operable range, or process envelope, has been developed through the pilot plant experience and the process simulation study. Based on the model predictions, an uncertainly range was defined in the design recommendations of a pioneer coal drying plant in scale-up.     

Vibration and Damping Characteristics of a Beam with a Partially Sandwiched Viscoelastic Layer

The purpose of this study is to verify the vibration and damping characteristics of a partially-layered elastic-viscoelastic-elastic structure both theoretically and experimentally.

The fourth-order differential equations of motion are derived for the transverse vibration of a three-layered sandwich beam with a viscoelastic (or adhesive) core layer. The transverse displacements of the constraining layer and the base beam are assumed to have different parameters. Both the transverse normal strain and the longitudinal shear strain of the viscoelastic core layer are included in the equations of motion. The solution to the resulting equations is obtained by solving a boundary value problem.

Numerical analysis of the equations and experimental measurements is illustrated by a cantilever beam in transverse vibration.

The vibration and damping effects of completely and partially covered beams are investigated and the effect of the position changes of partial coverage is intensively analyzed.     

INTERPOLATION BETWEEN TWO EXCESS GIBBS FREE ENERGY-COMPOSITION ISOTHERMS

It is shown in this paper how to interpolate a required excess Gibbs free energy-composition isotherm between two such given isotherms.

Efectively, our procedure employs semi-empirical equations for the excess Gibbs free energy, whose adjustable parameters can be identified with infinite dilution properties, and still be made to give close fits, to experimental data. Prediction of these infinite dilution properties is achieved through the use of a linear correlation between them and certain pure component properties. Thus in addition to the two given isotherms, the input into our theory consists of the Antoine vapor pressure constants, critical constants and acentric factors for the pure components.

Our theory has been tested against experimental data for four binary systems ranging from moderately non-ideal to highly non-ideal; the agreement is very good.

The successful execution of the present program highlights the possibility of predicting (g^E-x) isotherms, given limiting activity coefficients (determined chromatographically or otherwise), and a single data point for the equi-molar mixture.     

ULTRAFILTRATION FLUX AND REJECTION CHARACTERISTICS OF BLACK LIQUOR AND POLYETHYLENE GLYCOL

Comparative experimental studies were carried oul on ultrafiltration with black liquor, and polyethylene glycol as a standard molecule, using an asymmetric membrane in a stirred batch cell. Effects of pressure, concentration, and stirrer speed were studied on flux and salute rejection characteristics for both the solutes.

The experimental results were analysed using the osmotic pressure limitation model to account for concentration polarization. It was found that, apart from the rise in osmotic pressure with pressure and concentration, there was a uniform rise in the polarization layer resistance (R_p) with membrane surface concentration (c_m). The results were correlated by the equation:

where ∝ and βt are constants. The membrane was characterized by determining the solution permeability (P_m) and reflection coefficient (a). The value of a was found to be close to unity—a representative value for high rejection membranes.