bluuebunny/crossref_metadata_2025 huggingface dataset:
Theory of electrophoretic separations. Part II: Construction of a numerical simulation scheme and its applications
Authors: Palusinski O. A. , Graham A. , Mosher R. A. , Bier M. , Saville D. A.
Published: June 2004

The mathematical model outlined in Part I is recast in a form suitable for numerical computation. The spatial derivatives are replaced by finite‐difference expressions, which leads to a set of ordinary differential equations coupled to a set of nonlinear algebraic relations. This system is solved using existing integration techniques. The resulting algorithm simulates the characteristic behavior of the classical modes of electrophoresis, which is shown by examples involving moving boundary electrophoresis and isoelectric focusing. In the first example two different integration schemes are used and their accuracy and stability investigated. The second example illustrates the versatility of the methodology.
Computer simulation of a rotary dryer. Part I: Retention time
Authors: Kamke F. A. , Wilson J. B.
Published: June 2004

A computer model of a single‐pass, rotary‐drum dryer with or without a center‐fill flighting section, describes the drying behavior of wood particles within the drum. This part of a two‐part study examines retention time; the second part incorporates heat and mass transfer for the complete drying model. Simulation results with retention time data from a large‐scale rotary dryer showed a favorable comparison, with a root mean square error of 14.2%.
Computer simulation of a rotary dryer. Part II: Heat and Mass Transfer
Authors: Kamke F. A. , Wilson J. B.
Published: June 2004

A computer model of a single‐pass, rotary‐drum dryer with or without a centerfill flighting section, describes the drying behavior of wood particles within the drum. This part of a two‐part study examines heat and mass transfer, which are shown to be partly dependent on the pattern of particle flow and on retention time. Comparison of simulation results with drying data based on moisture content of outlet particles from a large‐scale rotary dryer was favorable, with a root mean square error of 22.2%.
A local composition model for the excess Gibbs energy of aqueous electrolyte systems
Authors: Chen Chau‐Chyun , Evans L. B.
Published: June 2004

The electrolyte nonrandom two‐liquid (NRTL) model proposed by Chen et al. (1982) is generalized to represent the excess Gibbs energy of aqueous multicomponent electrolyte systems. Using only binary parameters, the model correlates and predicts the deviation from ideality of aqueous multicomponent electrolyte systems over the entire range of temperature and concentration.
A mixed‐integer nonlinear programming algorithm for process systems synthesis
Authors: Duran M. A. , Grossmann I. E.
Published: June 2004

The problem of synthesizing processing systems via simultaneous structural and parameter optimization is addressed in this paper. Based on a superstructure representation for embedding alternative configurations, a general mixed‐integer nonlinear programming (MINLP) framework is presented for the synthesis problem. An efficient outer‐approximation algorithm is described for the solution of the underlying optimization problem, which is characterized by linear binary variables and continuous variables that appear in nonlinear functions. The proposed algorithm is based on a bounding sequence that requires the analysis of few system configurations, and the solution of a master problem that identifies new candidate structures. Application of the proposed algorithm is illustrated with the optimal synthesis of gas pipelines.
Interfacial area generated in aqueous electrolyte solutions on a sieve plate
Authors: Pohorecki Ryszard , Nowosielski Jan
Published: June 2004

A light depolarization method was used to measure the interfacial area of froth on a sieve plate. The effects of hydrodynamics and the presence of electrolytes on the magnitude of the interfacial area were studied. The results obtained for pure water and for two different aqueous solutions of inorganic salts were compared. In the case of aqueous electrolyte solutions the size distributions of ionic bubbles and the fraction of interfacial area contributed by these bubbles were determined by a photographic method. It was found that the interfacial area generated in aqueous electrolyte solutions was considerably (about 30%) greater than the interfacial area generated in pure water, and that about 45% of the total interfacial area in the former case was contributed by ionic bubbles which formed a separate population.
Drop breakup in turbulent stirred‐tank contactors. Part II: Relative influence of viscosity and interfacial tension
Authors: Wang C. Y. , Calabrese R. V.
Published: June 2004

The relative influence of dispersed‐phase viscosity and interfacial tension on equilibrium drop size and drop size distribution is studied for dilute suspensions by dispersing various silicone oils in water, methanol, and their solutions. Correlations for Sauter mean diameter, D32, are developed in terms of system variables using the mechanistic models of Part I. Drop sizes for low to moderate viscosity dispersed phases are normally distributed in volume and can be correlated by normalization with D32. Trends in the distributions are explained in terms of a parameter representing the relative resistance to breakage.
Effects of finely divided solids on mass transfer between a gas and an organic liquid
Authors: Bartos T. M. , Satterfield C. N.
Published: June 2004

Global gas‐liquid mass transfer parameters, kLa and a were determined in an organic liquid in which finely divided solid particles were suspended in a mechanically stirred vessel. The product kLa and a both decreased linearly with solids loading; both were independent of particle size and particle density. Gas holdup was independent of solids loading.
Separation of fine particle dispersions using periodic flows in a spining coiled tube
Authors: Papanu J. S. , Adler R. J. , Gorensek M. B. , Menon M. M.
Published: June 2004

A centrifugal method for fractionating fine (<10 μm) particles by size and/or density is described. Periodic, bidirectional flow through a continuously spinning coiled tube splits fine particle suspensions into two fractions. Proof‐of‐principle experiments with zeolite powder have demonstrated successful concentration of aqueous dispersions.
Vertical upward cocurrent gas‐liquid annular flow
Authors: Zabaras G. , Dukler A. E. , Moalem‐Maron D.
Published: June 2004

Upward cocurrent gas‐liquid annular flow was investigated in a 50.8 mm ID cylindrical vertical pipe. The film flow was studied by measuring instantaneous local film thickness, wall shear stress, and pressure gradient. Analysis of these data revealed that at low gas flow rates the film motion is controlled by a switching mechanism, as speculated by Moalem‐Maron and Dukler (1984). In the region of high gas flow rates the switching process is suppressed and traveling roll waves characterize the film motion.
Mass transfer and electrochemical kinetic interactions in localized pitting corrosion
Authors: Gaudet G. T. , Mo W. T. , Hatton T. A. , Tester J. W. , Tilly J. , Isaacs H. S. , Newman R. C.
Published: June 2004

Identification and characterization of coupled diffusional and electrochemical kinetics effects was achieved under potentiostatic anodic dissolution conditions. A one‐dimensional artificial pit geometry with sample wire electrodes embedded in an inert support exposed to NaCl solutions was used to study the dissolution of stainless steel and highnickel Alloy 600. Multiple steady states for both materials were determined at conditions where the diffusional transport rates balanced the electrochemical rate of dissolution at the surface of the wire electrode. A theoretical transport model was developed to quantitatively explain the observed multiple steady state phenomena.
Interaction analysis in multivariable control systems
Authors: Jensen N. , Fisher D. G. , Shah S. L.
Published: June 2004

Most published “interaction measures” can produce misleading results and often do not measure the true closed‐loop interaction. Therefore, closed‐loop transmittances are defined mathematically as direct, parallel, disturbance, and interaction transfer functions and it is shown that the direct Nyquist array design method includes an excellent basis for interaction analysis.
Rapid computation of chemical equilibrium composition: An application to hydrocarbon combustion
Authors: Erickson W. D. , Prabhu R. K.
Published: June 2004

A scheme for rapidly computing the chemical equilibrium composition of hydrocarbon combustion products is derived. A set of ten governing equations is reduced to a single equation that is solved by the Newton iteration method. Computation speeds are approximately 80 times faster than the often used free‐energy minimization method. The general approach also has application to many other chemical systems.
Immobilization of enzymes in porous solids under restricted diffusion conditions
Authors: Hossain Md. M. , Do D. D. , Bailey J. E.
Published: June 2004

A restricted diffusion model is developed to study the immobilization of enzyme in porous solid supports. Simulation studies have been carried out for various combinations of process variables and parameters of the immobilization system. The model has also been used to develop a method for estimating the intrinsic rate constant of immobilization when enzyme diffusion into the support is restricted. Results of experiments in which glucose oxidase was immobilized in porous glass supports are consistent with model simulations.
Diffusion in solids under strain, with emphasis on polymer membranes
Authors: Neogi P. , Kim Myungsoo , Yang Yun
Published: June 2004

A solute diffusing through a solid gives rise to a change in volume. This swelling can be viewed as a strain, and it is possible to obtain the accompanying stress using elasticity theory. The theory provides two ways by which stresses can be generated. The first comes from the condition of impenetrability where the system generates stress to exclude certain configurations during deformation. The second is due to imposed restrictions on the geometry during the swelling process. Larché and Cahn have provided the thermodynamics for such systems, from which the chemical potential can be used to obtain a phenomenological expression for flux and an expression for the solubility. These two are sufficient to obtain the sorption response in most systems. Solutions have been obtained here.
Connectivity effects for surface diffusion of adsorbed gases
Authors: Zgrablich G. , Pereyra V. , Ponzi M. , Marchese J.
Published: June 2004

Nonlocal models for the surface transport of adsorbed gases on solids are proposed and compared to experimental data. These models take into account connectivity effects due to heterogeneous adsorption potential surfaces and introduce a more realistic calculation of the surface mean free path.
Liquid phase oxidation kinetics of oil sands bitumen: Models for in situ combustion numerical simulators
Authors: Adegbesan K. O. , Donnelly J. K. , Moore R. G. , Bennion D. W.
Published: June 2004

Multiresponse kinetic models are established for the low‐temperature oxidation (LTO) reactions of Athabasca oil sands bitumen. The models provide adequate description of the overall rate of oxygen consumption and of the reactions of the liquid phase bitumen components. The LTO models are suitable for use in the in situ combustion numerical simulators of the oil sands.
Multicomponent adsorption equilibria of nonideal mixtures
Authors: Talu Orhan , Zwiebel Imre
Published: June 2004

Experimental gas‐solid adsorption measurements were made on the binary and ternary mixtures of H2S, CO2, and C3H8 on H‐mordenite molecular sieve zeolite at 30°C. The C3H8 containing binaries and the ternary mixture exhibited nonideal behavior, as evidenced by the azeotropelike crossovers in the composition domains and by the peaks in the total amount adsorbed surface. The ternary data were successfully predicted with the activity coefficients calculated by the spreading‐pressure‐dependent equation. Models that neglect the spreading‐pressure dependence can only qualitatively predict the nonidealities.
Effect of convective heat transfer and phase change on the stability of aluminium smelting cells
Authors: Taylor M. P. , Welch B. J. , McKibbin R.
Published: June 2004

This paper focuses on two aspects of smelting operation that are highly dependent on the rate of heat transfer in the molten bath. As a consequence of the elevated temperature and the corrosive nature of the fluoride mixture, the cell sidewalls are designed so that some electrolyte will freeze onto them, protecting the carbon from erosion and at the same time insulating the cell against excessive heat loss. The thickness and dynamic variation of this frozen ledge are determined by the convective heat transfer from the bath to the freeze surface.

Another situation where the rate of convective heat flow exerts a subtle influence is the dissolution of aluminium oxide powder in the bath. The localized feeding of large quantities of the powder causes transient electrolyte freezing on some of the added material, hindering its dissolution and causing the formation of an alumina sludge below the molten aluminium pad.
Droplet entrainment in vertical annular flow and its contribution to momentum transfer
Authors: Lopes J. C. B. , Dukler A. E.
Published: June 2004

Simultaneous measurements were made of the size and the axial and radial velocity of drops entrained by the gas in annular flow. A model is developed to use these data to compute the rate of deposition or entrainment and the pressure gradient, ▽ρE, due to drop interchange. ▽ρE is a significant fraction of the measured total gradient, ▽ρ.
Thermodynamics of hydrogen‐bonded molecules: The associated perturbed anisotropic chain theory
Authors: Ikonomou G. D. , Donohue M. D.
Published: June 2004

The perturbed anisotropic chain theory (PACT) developed by Vimalchand and Donohue has been generalized to treat pure fluids that associate through hydrogen bonding, as well as mixtures of one associating component and several diluents. Using an approach similar to that of Heidemann and Prausnitz, a closed‐form equation of state has been derived. It is applicable to simple as well as complex molecules at both gas and liquidlike densities and takes into account dipole and/or quadrupole moments. Molecular parameters were obtained by fitting the equation to experimental liquid density and vapor pressure data.
Turbulent flow in stirred tanks. Part II: A two‐scale model of turbulence
Authors: Placek Jiří , Tavlarides L. L. , Smith G. W. , Fořt Ivan
Published: June 2004

The two‐scale turbulence concept is recommended for modeling the turbulence in a baffled vessel equipped with a Rushton‐type turbine impeller. A three‐equation isotropic turbulence model is proposed that employs the balance equations for: the kinetic energy of the large scale vortices; the kinetic energy of the inertial subrange eddies; and the dissipation rate of the small‐scale turbulence. The energy transfer rate from the large‐scale vortices is prescribed algebraically. Flow patterns are modeled by solving the transport equations for vorticity, stream function, and tangential momentum. The Reynolds stresses are modeled by means of the effective viscosity, based on the three‐equation model of turbulence. The calculated profiles of the mean velocity at the tank wall agree with experimental data obtained in the same system by means of a Pitot tube.
Molecular thermodynamics for fluids at low and high densities. Part II: Phase equilibria for mixtures containing components with large differences in molecular size or potential energy
Authors: Cotterman R. L. , Prausnitz J. M.
Published: June 2004

The molecular‐thermodynamic correlation presented in Part I for pure fluids is extended to mixtures; this extension is particularly useful for mixtures of components with large differences in molecular size or potential energy. The novel feature of this correlation is a separation of the high‐density and low‐density contributions to the residual Helmholtz energy; this separation allows use of separate mixing rules for each density regime, guided by theoretically defined boundary conditions. Such flexibility is necessary to represent phase equilibria in highly asymmetric fluid mixtures such as water‐hydrocarbon systems. Phase equilibria are correlated for a variety of binary and multicomponent mixtures, including a petroleum reservoir fluid containing carbon dioxide and including a mixture of hydrogen and coal‐derived liquids.
Numerical analysis of jet‐stirred reactors with turbulent flows and homogeneous reactions
Authors: Liu Chih‐Hsiung , Barkelew C. H.
Published: June 2004

A computer program designed to model the turbulent reacting flow in jet‐stirred reactors has been developed. In solving the single‐phase flow field, a two‐equation turbulence closure was used to predict the turbulent eddy viscosity variation in the reactor. The model was used to predict the performance of a real reactor. The predicted results compared favorably with measurements in the field. It was found that the key to the reactor performance is the strength of the recirculating eddy caused by the jet entrainment.
Kinetics of hydrogen absorption in a stirred metal hydride slurry
Authors: Tung Yuanki , Grohse E. W. , Hill F. B.
Published: June 2004

Isothermal, isobaric measurements were made of the rate of hydrogen absorption by a slurry of LaNi5 powder suspended in n‐undecane in a baffled stirred reactor. The data were interpreted using a model emobodying three resistances in series: a gas‐liquid mass transfer resistance, a liquid‐solid mass transfer resistance, and an “overall reaction resistance.”

At the highest agitator speeds employed, 2,000 rpm, conversions of LaNi5 to hydride of 90% or better were obtained within one minute or less, thereby confirming the potential of the metal hydride slurry concept for commercial applications.
Designing hollow‐fiber contactors
Authors: Yang Ming‐Chien , Cussler E. L.
Published: June 2004

Hollow‐fiber contactors can provide fast mass transfer without flooding or loading. They are a promising alternative to packed towers for gas treating, and to centrifugal extractors for liquid‐liquid extraction. Hollow‐fiber contractors can be designed effectively using the mass transfer correlations reported in this paper. The correlations, based on aqueous deaeration and carbon dioxide absorption, are similar to earlier heat and mass transfer correlations, but can be complicated by diffusion across the fiber wall and by alterations in fiber geometry.
Diffusion and mass transfer in supercritical fluids
Authors: Debenedetti P. G. , Reid R. C.
Published: June 2004

The different behavior of fluid density and viscosity in going from the dilute gas to the dense fluid state gives rise to kinematic viscosities which, in the near supercritical region, are lower than for liquid metals. As a consequence, the relative importance of natural convection (as measured by the ratio of buyoant to inertial forces) is two orders of magnitude higher in a supercritical fluid (at constant Reynolds number) than in normal liquids.

Binary diffusion coefficients of nonvolatile solutes in supercritical fluids were measured with a technique that involved laminar flow and diffusion in a rectangular channel. The solution to this hydrodynamic problem is presented. By varying the inclination of the solute source plane with respect to the horizontal position, apparent diffusion coefficients were measured that were up to six times higher than the “true” coefficients.

Experimental binary diffusion coefficients, including published literature data, were analyzed in the light of hydrodynamic (Stokes‐Einstein) theory. The analysis suggests that under the high‐density, low‐viscosity conditions that characterize supercritical fluids, hydrodynamic behavior at the molecular level is approached, and can be used as a basis for data extrapolation.
Internal model control of coupled distillation columns
Authors: Levien K. L. , Morari Manfred
Published: June 2004

An experimental evaluation of methods to analyze process resilience based on internal model control (IMC) has been performed. A pilot plant consisting of two coupled distillation columns was instrumented for control studies using an LSI 11/23 microcomputer. Two alternative sets of inputs were chosen and the two full 7 (all outputs) × 4 (all inputs) transfer matrix models of the pilot plant were identified. From these models, a large number of potential 3 × 3 control structures were first screened for different levels of achievable control performance using the newly developed tools for resilience analysis. Without the need for simulation and with minimal computational effort these new techniques allow prediction of the effect of nonminimum phase characteristics, input constraints, and model uncertainty on achievable closed‐loop performance. The resilience analysis results were found to be in agreement with qualitative physical intuition. To more fully investigate the usefulness and precision of the resilience analysis, three control structures for maintaining three product compositions from a distillation system were studied experimentally. The design and performance of IMC for this complex system is demonstrated and compared with single‐loop PID controllers combined with a dynamic decoupler.
Chaos during the electrodissolution of iron
Authors: Diem C. B. , Hudson J. L.
Published: June 2004

Experiments were carried out on the electrodissolution of iron from a disk electrode rotating at 900 rpm in 1 M H2SO4. Current was measured as a function of applied potential. Potentiostatic current oscillations, all of which were chaotic, occurred over a range of applied potential. The characteristics of these chaotic oscillations were studied with the aid of state space plots and Poincaré sections, and with the calculation of ν, the correlation dimension; the latter quantity varied smoothly between 2.4 and 6.0 throughout the range of applied potential studied. The attractor for which ν = 2.4 can be represented by a three‐dimensional state space plot.
Steady state phenol degradation in a draft‐tube, gas‐liquid‐solid fluidized‐bed bioreactor
Authors: Tang Wen‐Tzung , Fan Liang‐Shih
Published: June 2004

Experiments on phenol biodegradation by a mixed culture in a draft‐tube, three‐phase fluidized‐bed biofilm reactor (DTFBR) at the steady state were performed. The characteristics of biofilms developed in the DTFBR were identified. A steady state biofilm model was proposed that considers the simultaneous diffusion and reaction of oxygen and phenol within the biofilm and the external mass transfer resistance between the biofilm and the completely mixed bulk liquid phase. The proposed model assumes a double‐substrate limiting mechanism for microbial growth kinetics, and Haldane and Monod type expressions were used to characterize the dependence of microbial specific growth rate on phenol and oxygen, respectively. The experimental results were used to test the validity of the proposed model.
Kinetics of dissolution of alumina in acidic solution
Authors: Franke M. D. , Ernst W. R. , Myerson A. S.
Published: June 2004

The dissolution kinetics of alumina in aqueous solution was studied in batch and continuous systems. Data were correlated by the kinetic equation C(t) = 1 − exp(−ktα). The parameter k was a function of temperature and acid concentration, while the parameter α remained constant.

The temperature variation of k was accurately represented by an Arrhenius‐type equation with a temperature coefficient, 18,200 kJ/kmol. The data obtained in batch experiments were free of mass transport and mixing effects. Adsorption‐desorption equilibrium of hydrogen ion at the alumina surface was observed. The results supported postulated reactions reported in the literature for alumina dissolution. The basic features of the mechanism include hydration of the aluminum oxide surface, hydrogen ion adsorption followed by reaction to form a positively charged surface species [Al(OH)2+], formation of stable surface species [AlOOH and (Al(OH)2)2 SO4], and desorption of products.
Wall and interfacial shear stress in stratified flow in a horizontal pipe
Authors: Kowalski J. E.
Published: June 2004

Experimental values are presented for the wall and interfacial shear stresses in stratified gas‐liquid flow in a pipe. The wall and Reynolds shear stresses were measured using a hot‐film anemometry technique. The interfacial shear stress was determined using two methods: from a momentum balance, using the wall shear stresses and void fraction measurements, and from an extrapolation of the Reynolds shear profile at the gas‐liquid interface. The predicted interfacial shear stress data were approximated by the formula relating the interfacial friction factor with the void fraction and gas and liquid Reynolds numbers, and were compared with other reported data.
Influence of interfacial waves in stratified gas‐liquid flows
Authors: Andritsos Nikolaos , Hanratty T. J.
Published: June 2004

Interfacial stresses are calculated from new measurements of liquid height and pressure drop for fully developed horizontal stratified flow. These are related to wave properties. An improved design method is suggested.
Mathematical modeling of pulsing flow in large trickle beds
Authors: Sundaresan S.
Published: June 2004

A crossflow model for pulsing flow in a trickle bed of large cross section is presented. The trickle bed is idealized as being made up of pulses and the trickling flow region surrounding these pulses. Assuming the macroscopic gas flow around the pulses to be irrotational and the pulses to contain only liquid, the model equations are derived. An analysis of the model and comparison with the experimental results of Christensen (1986) reveals that the irrotational flow model underestimates the pulse velocity for realistic pulse shapes. This can be attributed to the underestimation by the model of the drag exerted by the trickling region on the pulses. By dropping the irrotational flow assumption and viewing the model as semiempirical, a single parameter characterizing the magnitude of this drag is estimated from the pulse velocity data. When this estimated value for this parameter is employed, the model predicts the average pressure gradient data reasonably well.
Ternary gas mixture separation in two‐membrane permeators
Authors: Sengupta A. , Sirkar K. K.
Published: June 2004

Single‐stage separation of ternary gas mixtures of He, CO2, and N2 in a hollow‐fiber permeator that simultaneously houses two different types of membranes, cellulose acetate and silicone rubber, was investigated. The two membranes have reverse selectivities with respect to He and CO2. Such a two‐membrane permeator separates the feed into three streams, two permeates and one reject, each stream being enriched in a different component. The species permeabilities through each membrane were measured independently, and these values were utilized in a simulation that incorporates the fiber lumen pressure drops, the elastic deformation of the silicone capillaries, and the asymmetric structure of the CA membrane. Simulation results are compared with experimental data. Effects of flow pattern, relative permeation areas of the two membranes, permeate pressure ratios, feed composition, and membrane selectivities are studied. Advantages of the two‐membrane scheme over the conventional permeators with only one kind of membrane are discussed.
Dissolution and reprecipitation in model systems of porous hydroxyapatite
Authors: Kim Jeung Lark , Cussler E. L.
Published: June 2004

Studies of the attack of gel‐stabilized suspensions of hydroxyapatite show dissolution at the boundary of the solid region and reprecipitation within this region. The results are apparently consistent with a theory which assumes that porous solid dissolution is diffusion‐controlled but constrained by nonlinear solubility products.
Toward a molecular equation of state for real materials
Authors: Fleming P. D. , Brugman R. J.
Published: June 2004

An equation of state based on molecular interaction concepts has been developed. This equation contains three parameters corresponding to a square‐well potential characterized by a molecular radius, a well depth, and a well width. It is obtained by perturbation theory with a hard sphere reference system and, with appropriate choice of parameters, yields good agreement with experimental PVT properties of 12 nonaqueous substances. The agreement is in all cases for superior to that obtained with the usual implementation of the Peng‐Robinson equation, and is better for most cases than that obtained by optimizing the parameters in the Peng‐Robinson equation.

For water, neither the reported equation nor the Peng‐Robinson equation is in agreement with experiments. To obtain acceptable agreement, it is necessary to employ an equation that treats the particular geometry of attractive interactions characteristic of water. The Fleming‐Gibbs lattice equation of state for water does give reasonable agreement with PVT properties.
Theory and measurement of hydrate dissociation
Authors: Ullerich J. W. , Selim M. S. , Sloan E. D.
Published: June 2004

Experimental data on the rate of dissociation of methane hydrates are presented. The data were obtained from hydrate mass loss measurements using an electrobalance. A resistance heater with a known heat flux was used in the dissociation experiments. A mathematical model describing the dissociation process is also presented. The model, based upon first principles, assumes that the water formed during dissociation is blown away by the methane gas produced so that the dissociation process may be regarded as a moving‐boundary ablation problem. Agreement between the model and the data is within 10%.
The isothermal flash problem: New methods for phase split calculations
Authors: Ammar M. N. , Renon H.
Published: June 2004

Various numerical approaches have been adopted to solve the single‐stage isothermal flash problem. These approaches result in two classes of methods. The first includes equation‐solving methods that try to solve a nonlinear equation system; the second is based on a minimization of the total Gibbs free energy. Most of these methods may fail to find a solution or may lead to erroneous solutions near critical conditions when an equation of state is applied to both the vapor and liquid phases.

New methods for solving the problem are proposed. Combining the simplicity in structure of the conventional successive‐substitution method and the efficiency of some unconstrained minimization algorithms, they all ensure convergence to local minima of the Gibbs free energy. The new methods are compared from the standpoints of computer storage and calculational effort requirements. The performance of these methods is tested on four multicomponent systems taken from literature, and a comparison is made with other published methods.
Droplet dynamics in vertical gas‐liquid annular flow
Authors: Lopes J. C. B. , Dukler A. E.
Published: June 2004

Data for the two‐dimensional velocity and size of entrained drops carried by the gas core during upward annular gas liquid flow are presented. The measurements of velocity and size were made simultaneously using a new experimental technique. Information on the variation of the drop velocity with flow rates, radial position in the core, and drop size are presented and analyzed. Droplet velocity is shown to increase with size, counter to intuitive expectation. This is explained in terms of highly modified drag‐Reynolds number relationships caused by the high turbulence level in the core.
A rule‐based approach to fault diagnosis using the signed directed graph
Authors: Kramer M. A. , Palowitch B. L.
Published: June 2004

Fault diagnosis is the problem of determining the root causes of process upsets. This paper presents a very efficient method of identifying the possible causes of process disturbances using the signed directed graph (digraph) representation of process interactions. The analysis is based on forming logical statements (rules) derived from the process digraph; these are evaluated using on‐line data to yield the diagnosis. Evaluation of rule antecedents is more efficient than the previous algorithmic approach of Shiozaki et al. In the rule‐based approach, the diagnostic criteria are represented explicitly, not hidden by a complex algorithmic procedure. This allows the diagnostic rules to be tailored to reflect the best available knowledge of plant behavior. The rules generated by this technique can be integrated with other rules on plant operations using an expert systems framework.
Intraparticle diffusion coefficients in packed columns: Measurement by arrested‐flow gas chromatography
Authors: Park In‐Soo , Smith J. M. , McCoy B. J.
Published: June 2004

Arrested‐flow chromatography was used to determine intraparticle diffusivities of large‐pore particles packed in columns. Particle and column tortuosity factors were determined for helium tracer in nitrogen carrier gas at 40°C and atmospheric pressure. Semiempirical modifications of Maxwell's, Burger's, Jeffrey's, and Rayleigh's relations for the composite diffusivity of spherical particles in a stationary medium are proposed for the effective composite diffusion coefficient for a packed bed of porous particles. The equations, modified to represent accurately the extraparticle void diffusion based on measurements for beds of nonporous particles, are used to evaluate intraparticle diffusivities from experimental data obtained by arrested‐flow chromatography.
Total and radiative heat transfer to an immersed surface in a gas‐fluidized bed
Authors: Mathur Ajay , Saxena S. C.
Published: June 2004

A high‐temperature heat transfer probe capable of measuring both the total and radiative heat transfer coefficients between an immersed surface and the bed has been designed, fabricated, and tested. Measurements of these coefficients in beds of 559 and 751 μm sand particles at temperatures up to 1,175 K have been made using this probe. A thermal analysis of the probe is developed in order to ensure a reliable interpretation of the measured quantities. The dependence of the total and radiative heat transfer coefficients on such parameters as bed temperature, fluidizing air velocity, and mean bed particle size are investigated. The various models proposed to describe high‐temperature heat transfer are evaluated from this perspective. The models capable of best simulating the heat transfer process with relative ease of computation are identified and evaluated using data generated in the study.
Chemically reactive generalized Taylor dispersion phenomena
Authors: Shapiro Michael , Brenner Howard
Published: June 2004

Generalized Taylor dispersion theory for nonreactive solutes (Brenner 1980a; 1982) undergoing convection and diffusion is extended to include irreversible first‐order volumetric and surface chemical reactions possessing position‐dependent reactivity coefficients at the microscale. For sufficiently long times the equivalent chemical kinetic description of the rate of solute depletion at the macroscale is shown to manifest itself as a single constant reactivity coefficient K̄* characterizing an apparent first‐order irreversible volumetric reaction. Subtraction of this gross solute depletion rate from the original microscale transport equation permits the resulting Taylor dispersionlike problem to be resolved by a solution scheme closely paralleling that for the comparable nonreactive case. This allows a straightforward determination of the mean global solute velocity vector Ū* and dispersivity dyadic D̄* appearing in the macroscale convection‐diffusion‐reaction equation describing the local‐space averaged mean transport process. By way of example, these three coefficients are explicitly calculated for reacting and diffusing solute particles sedimenting from a solvent flow occurring between two parallel plates onto the reactive surface of one of these plates.
Reaction kinetics and reactor modeling of the plasma etching of silicon
Authors: Stenger H. G. , Caram H. S. , Sullivan C. F. , Russo W. M.
Published: June 2004

A model including the effects of diffusion and convection can be used to predict the etch rate of crystalline silicon in a plasma discharge of nitrogen trifluoride. The case of a radial flow reactor with crystalline silicon wafers located at discrete positions can be solved using a finite‐element solution to a boundary value problem. Such a model is useful to predict the effects of pressure, flow rate of etchant gas, percent silicon exposed, and wafer position on both inter‐and intrawafer etch rates. It was found from modeling that greater uniformity in etch rate is achieved by lowering the pressure and percent exposure of silicon, and to a lesser degree the volumetric flow rate.
Mineral sequences in precipitation/dissolution waves
Authors: Bryant S. L. , Schechter R. S. , Lake L. W.
Published: June 2004

A theory for flow through permeable media with equilibrium precipitation/dissolution interactions is rigorously established. The general solution in terms of waves, which represent the propagation of concentration changes is developed, and the detailed structure of a precipitation/dissolution wave in the presence of dissipation (diffusion and dispersion) is derived; this structure plays a vital role in the general solution. The solution is based on Riemann invariants and thus exhibits certain similarities to wave solutions of related problems in gas dynamics and chromatography. However, a discontinuity peculiar to the precipitation/dissolution problem prevents unification of these similar solutions into a single, more general theory.
Hydrodynamics of electroluidization: Separation of pyrites from coal
Authors: Shih Y. T. , Gidaspow Dimitri , Wasan Darsh
Published: June 2004

Dry, electrostatic separation is a potentially efficient method of removing pyrites from coal. However, progress in the past was hampered by a lack of a quantitative analysis of the process. To help us design better separation equipment, we have developed a hydrodynamic model of separation of pyrites from coal in a batch electrofluidized bed. The simulations were done on a Cray‐2 computer. The input variables include the surface charge of the particles and the solids stress, which were measured.

Realistic shapes and sizes of bubbles were computed with and without an applied electric field for a two‐dimensional bed with a central jet. The bubble sizes and the rising velocities were smaller with an applied field, consistent with observations. Computed electrophoretic mobilities in the fluidized bed will be useful for a better design of continuous beds.
Mass transfer in nitric acid absorption
Authors: Miller D. N.
Published: June 2004

The mechanism and rate limitations in aqueous nitrogen oxides absorption are reviewed and data available on chemical kinetics for performance predictions are discussed. Application of a rate relationship to characterize interphase mass transfer for the primary reactant N2O4 is shown, with mass transfer coefficients derived from plant‐scale data. Correlations for these coefficients as functions of acid strength and temperature for both bubble cap and sieve plate designs are presented.
A vapor pressure equation from extended asymptotic behavior
Authors: Iglesias‐silva G. A. , Holste J. C. , Eubank P. T. , Marsh K. N. , Hall K. R.
Published: June 2004

The vapor pressure equation proposed here possesses several interesting features and does an excellent job representing data. The currently accepted theoretical behavior in the regions of the triple point and the critical point are intrinsic features of the expression. The equation is valid over the entire range from the triple point to the critical point and yet possesses only three adjustable constants. Results are presented for a small but chemically diverse set of compounds. This work represents an extension of the Churchill‐Usagi correlation technique from heat transfer and fluid mechanics to thermodynamics.
Effect of interfacial viscosities upon displacement in sinusoidal capillaries
Authors: Giordano R. M. , Slattery J. C.
Published: June 2004

This quantitative analysis shows the relative effects of interfacial tension, interfacial viscosities, and wetting during displacement in a capillary whose radius is a sinusoidal function of axial position. The effect of the interfacial viscosities is to increase the resistance to displacement regardless of the wetting condition. The result are consistent with a previous qualitative analysis and with a previous quantitative analysis for displacement in capillaries whose radii are independent of axial position.

In screening surfactant systems for potential use in tertiary oil recovery, it is recommended that the interfacial tension be minimized first, since it determines whether oil displacement will occur, and that the interfacial viscosities be minimized second, since they influence the rate of oil displacement.
Transport of particulate suspensions in porous media: Model formulation
Authors: Sharma M. M. , Yortsos Y. C.
Published: June 2004

A mathematical model is formulated for the general class of problems that involve the transport of stable particulate suspensions in porous media. The porous medium is represented by a network of pore bodies (sites) and pore throats (bonds). Population balances for the species responsible for particle retention and permeability reduction are written in terms of the various mechanisms of particle capture and reentrainment. Rates of capture and release are evaluated using appropriate physical models. We specifically concentrate on mass transfer limited processes. The effective‐medium theory is suitably formulated to determine the fluid flow distribution in the network and to calculate the permeability. The network representation of the porous medium together with the population balances and the rates of deposition and release provide a consistent model that finds application in filtration and fines migration processes.
Pore distribution changes of calcium‐based sorbents reacting with sulfur dioxide
Authors: Gullett B. K. , Bruce K. R.
Published: June 2004

Changes in the pore structure of calcium oxide sorbents derived from calcium carbonate (c‐CaO) and calcium hydroxide (h‐CaO) reacting with sulfur dioxide are determined. Results show that the pore shape of c‐CaO approximates a cylinder while that of h‐CaO appears to be slit‐ or platelike. The pore volume of c‐CaO is located in much smaller pores than that of h‐CaO when compared on the basis of an equivalent pore shape model. The effect of sintering was to reduce surface area through coalescence of smaller pores, while only minor effects were observed upon pore volume and conversion from calcium oxide to calcium sulfate. Both sorbents expand to allow greater reaction than is possible given the initial porosity and formation of a larger volume product. The h‐CaO reacts to higher levels of conversion than the c‐CaO because the pore shape of the h‐CaO allows for greater particle expansion and, therefore, reaction beyond the limits of the initial porosity.
Pool boiling from a surface with a porous layer
Authors: Lu S. M. , Chang R. H.
Published: June 2004

Boiling heat transfer from a porous layer sintered on a horizontal heater surface and heated from the base was analyzed for laminar to turbulent regions. The effects of the thickness of the porous layer, particle diameter, porosity, pore size distribution, and the properties of fluids on boiling heat transfer were analyzed. Reynolds number, parameter ψ, and a dimensionless heat flux were related to each other. Most experimental data used in this work fall in the region where the vapor Reynolds number is less than 100; very few data exceeded far beyond 1,000.

For thick porous beds, the thickness no longer affects the heat transfer. For thin porous beds, heat transfer is affected by the thickness of the porous layer. The prediction equations of various investigators for dryout heat flux were put into dimensionless forms and the differences that exist among the equations are explained.
Interpretation of the sulfation rate of CaO, MgO, and ZnO with SO2 and SO3
Authors: Kocaefe Duygu , Karman Deniz , Steward F. R.
Published: June 2004

Published models for gas‐solid reactions have been used with certain modifications to interpret sulfation data for CaO, MgO, and ZnO with SO2 and SO3. None of the models evaluated gave an adequate interpretation for high solid conversions, which were found to exceed 90% in some cases. Such high conversions are inconsistent with the current models, and a new mechanism must be postulated to explain the reaction after the solid product theoretically fills the initial pores of the particle. An important factor in successfully interpreting the experimental data is the distributed nature of the pore sizes within the solid particle.
Parametric sensitivity in fixed‐bed reactors: Inter‐ and intraparticle resistance
Authors: Morbidelli Massimo , Varma Arvind
Published: June 2004

The role of inter‐ and intraparticle transport resistances in the sensitivity behavior of a fixed‐bed catalytic reactor is fully elucidated. The parametric sensitivity regions obtained using a heterogeneous one‐dimensional plug flow model are reported for various values of the involved dimensionless parameters. Comparisons with previous sensitivity criteria and with experimental data are also presented.
Finite‐element steady state simulation of multiphase distillation
Authors: Swartz C. L. E. , Stewart W. E.
Published: June 2004

A finite‐element method is given for efficient simulation of multiphase distillation systems. Breakpoints are adaptively located to coincide with phase discontinuities. Thermodynamic criteria for the states at these discontinuities are included in the equation system. The adjustable breakpoint locations are calculated simultaneously with the other system variables by global Newton iteration. Worked examples demonstrate the accuracy and efficiency of the method.
Concept of system similarity in chemical engineering
Authors: Kubic W. L. , Stein F. P.
Published: June 2004

Fuzzy set theory is used to describe similarity of chemical engineering systems. The development of system similarity is given, and methods of determining a similarity relation are discussed. The system similarity relation is applied to the problems of measuring correlation confidence and quantifying modeling error. Sample problems are examined.
Mass transfer and solubility in autocatalytic oxidation of cyclohexane
Authors: Suresh A. K. , Sridhar T. , Potter O. E.
Published: June 2004

Mass transfer coefficients for the solution, without reaction, of oxygen in cyclohexane over a wide range of temperature and pressure have been measured in a flat interface reactor (FIR) and a gas sparged stirred‐tank reactor (STR). Solubilities have also been measured and it is suggested that a modified Henry's law coefficient of 1.09 × 10−2 kmol/m3 · bar can be regarded as constant over the temperature range 293–435 K. The physical mass transfer coefficient in the STR shows very little variation over this temperature range and a value of 3.5 × 10−4 m/s can be assumed for 423–435 K. However, coefficients in the FIR increase with agitation rate as expected. The difference is ascribed to interference by neighboring bubbles in the transfer process, when diffusivities are high, and also to the lowering of surface tension at high temperatures. A model proposed by Gal‐Or and Resnick is reviewed in its application to the present system.