Showing papers in "Chemical Engineering Science in 1991"
TL;DR: In this paper, the key concepts involved in powder precipitation are discussed, where the thermodynamics of phase transformation is discussed, and sections on nucleation and growth follow, with the subject of crystal shape reviewed.
Abstract: This article, which discusses the key concepts involved in powder precipitation, is organized in the following manner: After an introduction, where the thermodynamics of phase transformation is discussed, sections on nucleation and growth follow. With the kinetics established, the subject of crystal shape is reviewed. Following this, sections on particle morphology and size distributions are presented, which consider the population balances of idealized industrial reactors.
494 citations
TL;DR: In this paper, the equilibrium swelling behavior of hydrogels sensitive to pH or ionic strength changes of the swelling medium was studied using new structural models which are based on the Flory-Huggins thermodynamic theory, the rubber elasticity theory, and ionic interaction deviations therefrom.
Abstract: The equilibrium swelling behavior of hydrogels sensitive to pH or ionic strength changes of the swelling medium was studied using new structural models which are based on the Flory—Huggins thermodynamic theory, the rubber elasticity theory, and ionic interaction deviations therefrom. The number average molecular weight between crosslinks was related to equilibrium swelling characteristics, the thermodynamic compatability of the polymer—swelling agent system, the ionic charges, the pKa of the ionizable polymer moieties, and the pH and ionic strength of the surrounding medium. The models have predictive, correlative and design capabilities.
485 citations
TL;DR: In this paper, a method is proposed for the determination of the connectivity of porous solids, such as adsorbents and catalyst supports, from the analysis of nitrogen sorption measurements based on the use of percolation theory to analyse sorption hysteresis.
Abstract: A method is proposed for the determination of the connectivity of porous solids, such as adsorbents and catalyst supports, from the analysis of nitrogen sorption measurements. The new method is based on the use of percolation theory to analyse sorption hysteresis. For solids giving hysteresis loops of the International Union of Pure and Applied Chemistry (IUPAC) types H1 and H2, the mean coordination number of the pore network is determined by detecting and quantifying a percolation transition in the desorption isotherm. For type H3 hysteresis loops, an upper bound is obtained for the mean coordination number, although for some solids this bound is too high to be useful. No connectivity information can be obtained from the type H4 hysteresis loop. The analysis method is robust and can be applied routinely.
377 citations
TL;DR: In this paper, a general formulation for power absorbed in a homogeneous, isotropic multilayered medium exposed to plane waves from both faces has been developed, and temperature profiles obtained by solving the transient heat conduction equation with the microwave power as a source term.
Abstract: Microwave heating of food systems have conventionally been modeled based on a Lambert law formulation of the absorbed power. However this is strictly valid for semi-infinite samples only. The correct power dissipation must be computed from maxwell's equations. To determine the conditions of the approximate applicability of Lambert's law for finite slabs, we have compared it with the microwave heating predicted by Maxwell's equations. We have found that the critical slab thickness L crit (in cm) above which the Lambert law limit is valid can be estimated from L crit = 2.7 β −1 - 0.08, where the penetration depth, β −1 , is the distance in cm from the sample surface where the field reduces to 1/ e of its incident intensity. Temperature profiles calculated with the Lambert law limit for slabs thicker than L crit are within 0.5% of those predicted with the power calculated from Maxwell's equations. Using Maxwell's equations we have developed a general formulation for power absorbed in a homogeneous, isotropic multilayered medium exposed to plane waves from both faces. We report temperature profiles obtained by solving the transient heat conduction equation with the microwave power as a source term. Thermal and dielectric properties are assumed to be temperature-independent.
263 citations
TL;DR: In this paper, the authors present experimental results obtained in an accelerated carbonation apparatus using a variety of techniques, including TGA, and extend the mathematical model developed recently to include the entire range of ambient relative humidities.
Abstract: Carbonation of concrete is the major time-limiting factor for the durability of reinforced concrete structures. The carbonation reaction between atmospheric CO 2 and Ca(OH) 2 of the concrete mass destroys the high pH environment of surrounding concrete which protects the steel bars of reinforced concrete from corrosion. In this paper we present experimental results obtained in an accelerated carbonation apparatus using a variety of techniques, including TGA, and we extend the mathematical model developed recently to include the entire range of ambient relative humidities.
260 citations
TL;DR: In this paper, a compilation of data and model interpretation of CO2 absorption/desorption with mixtures of MDEA (methyldiethanolamine), MEA (monoethanolamine), and DEA (diethanoline) was presented.
Abstract: This paper presents a compilation of data and model interpretation of CO2 absorption/desorption with mixtures of MDEA (methyldiethanolamine), MEA (monoethanolamine) and DEA (diethanolamine). The electrolyte-NRTL model is used to represent the activity coefficients of the species in solution. The simplified eddy diffusivity theory is used to simulate liquid-phase hydrodynamic characteristics. Binary interaction parameters for the equilibrium model and kinetic rate constants have been regressed from literature and currently obtained experimental data. The data presented in this work include both absorption and desorption conditions and temperatures ranging from 288 to 313 K. The results indicate that the combined mass transfer/equilibrium model can effectively represent CO2 mass transfer rates for the mixtures MEA/MDEA and DEA/MDEA under a wide range of conditions. Using a generalized framework for consistency between kinetics and reation equilibria in nonideal systems, absorption and desorption data have been reconciled by allowing the forward rate constants to “increase” with ionic strength. It is shown that MDEA promotes the DEA reaction rate, but not the MEA reaction rate. Both of these phenomena can be explained in terms of the zwitterion mechanism for amine carbamate formation.
203 citations
TL;DR: In this article, the effect of pressure on the hydrodynamics of trickle-bed reactors is investigated, and two new correlations for the pressure drop and the liquid hold-up for non-foaming liquids are proposed; they are based on 1500 experimental results.
Abstract: The effect of pressure on the hydrodynamics of trickle-bed reactors is investigated. The two-phase pressure drop and the liquid hold-up (liquid RTD determination) were measured for pressures up to 8.1 MPa. The influence of pressure, gas and liquid flow rates, viscosity, the coalescence behaviour of the liquid, and the particle size was examined. The experimental results were compared to correlations from the literature and two new correlations for the pressure drop and the liquid hold-up for non-foaming liquids are proposed; they are based on 1500 experimental results. Consideration of systems exhibiting non-foaming behaviour shows that the two-phase pressure drop is correctly described by the introduction of the modified Lockhart and Martinelli parameter. The liquid saturation data analysis shows that this hydrodynamic parameter is pressure-independent for very low gas superficial velocities allowing for an acceptable estimation at atmospheric pressure.
190 citations
TL;DR: Modelling methods for modeling drug transport in tissue in the vicinity of a continuous source found molecules that are water-soluble, slowly eliminated, and diffusible are the best candidates for polymeric delivery to brain tissues.
Abstract: By providing a long-term and localized source of active drug molecules, controlled release polymer implants may reduce the systematic side effects and dose-to-dose variability associated with conventional drug administration. Implants may be particularly relevant for delivery of drugs to the brain, where therapy is frequently limited by the blood brain barrier. To aid in the design and application of new delivery systems, we developed methods for modeling drug transport in tissue in the vicinity of a continuous source. Transport was assumed to occur by diffusion with elimination due to irreversible metabolism reversible binding to fixed tissue components, or partitioning into capillaries. For polymer implants where diffusion in the polymer determines the rate of drug release, the rate of drug release from the polymer, drug concentration in the tissue, and drug penetration depend on rates of elimination and diffusion. Qualitatively similar results were obtained for degradable polymers. Model predictions were also used to interpret previously published data on the delivery of the steroid dexamethasone from an ethylene—vinyl acetate copolymer implant in rat brain. In general, molecules that are water-soluble, slowly eliminated, and diffusible are the best candidates for polymeric delivery to brain tissues. In contrast to conventional modes of administration, rapid permeation of active molecules through brain capillaries is the most significant barrier to effective drug distribution in the brain.
171 citations
TL;DR: In this article, the authors performed experiments on evaporation kinetics of droplets of water, colloidal silica, sodium sulphate and skimmed milk, and the experimental procedure was similar to that proposed by Charlesworth and Marshall (1960, A.I.Ch.E.J.6, 9−23).
Abstract: This paper presents research on evaporation of droplets containing dissolved or dispersed solids. Experiments on evaporation kinetics of droplets of water, colloidal silica, sodium sulphate and skimmed milk were performed. The experimental procedure was similar to that proposed by Charlesworth and Marshall (1960, A.I.Ch.E.J.6, 9–23). Individual droplets were suspended in a controlled air stream and their weight and temperature were measured as evaporation progressed. Video recording of the size and appearance of the droplets was made with magnification close to 100. The temperature was followed by a micro-thermocouple, while the mass was measured by using the deflection of a calibrated glass filament balance. Experimental data were compared with a computer simulation based on a model of heat and mass transfer, both within the droplet and from the droplet surface to surrounding air. Analytical and numerical solution of the set of equations was tested. A good agreement between experimental results and the numerical predictions for a variety of evaporation regimes is reported. Diffusion coefficients for three tested materials are determined. The model includes all stages of evaporation: initial heating and evaporation, quasi-equilibrium evaporation, crust formation and growth, boiling, and porous particle drying. Stage transition criteria are defined.
170 citations
TL;DR: In this paper, the authors analyzed the effect of the square cross-section of a capillary by viewing both side and diagonal planes of the capillary in order to analyze the effect.
Abstract: Coating the walls of a capillary is usually done in two steps: (1) wetting or filling the capillary with a viscous fluid, and (2) clearing the capillary by forcing air through it. Clearing amounts to driving the wetting viscous fluid out of the capillary by another immiscible fluid. When air is blown into one end of a tube containing the viscous fluid, a “bubble” forms with the back end open. The bubble travels down the tube forcing some of the liquid out and leaving behind a fraction, in the form of a uniform film covering the walls. This paper reports flow visualization in capillaries of square cross secton. Visualization of the bubble was done by viewing both side and diagonal planes of the capillary in order to analyze the effect of the square cross section. Measurements from the captured images were used to characterize the shape of the fluid—fluid interface. The coating thickness of liquid deposited on the capillary walls was measured as the fraction of the capillary volume occupied by the liquid. The results for a wide range of capillary numbers show that this fraction increased monotonically with increasing capillary number, approaching an asymptotic limit of 0.64. Sequential particle tracking techniques were used to determine the flow field in different regions surrounding the bubble. A semi-quantitative comparison of the flow behavior, in capillaries of square and circular cross section, has been carried out.
170 citations
TL;DR: In this article, the influence of increased gas density on the gas holdup in bubble column reactors was analyzed and a simple model for describing the holdup was also proposed, showing that the major effect of increasing gas density is to stabilize the regime of homogeneous bubble flow and, consequently, to delay the transition to the churn-turbulent flow regime.
Abstract: The aim of this study was to develop a practically usable model to describe the influence of increased gas density on the gas holdup in bubble column reactors. In order to develop an insight into this effect, we performed extensive sets of experiments at pressures ranging from 0.1 MPa to 2 MPa and with several gases (nitrogen, carbon dioxide, argon, helium and sulphur hexafluoride) in de-ionized water in a 0.16 m diameter bubble column. A careful analysis of the experimental results shows that the major effect of increased gas density is to stabilize the regime of homogeneous bubble flow and, consequently, to delay the transition to the churn-turbulent flow regime. The superficial gas velocity at this regime transition point, Utrans, was found to be a unique function of the gas density, encompassing both effects of pressure and molar mass. To elucidate the hydrodynamics in the two regimes, dynamic gas disengagement experiments were carried out in a 0.19 m diameter bubble column with four liquids (water, turpentine, n-butanol and mono-ethylene glycol) using nitrogen at 0.1 MPa. These results showed that the churn-turbulent regime is characterized by a bi-modal bubble size distribution, consisting of fast rising large bubbles (typically 5 cm diameter or larger) and small bubbles (typically ⩽ 5 mm diameter). In the churn-turbulent regime the holdup of the small bubbles was found to be virtually constant. The regime transition velocity Utrans was found to depend on the liquid properties. A simple model for describing the gas holdup is also proposed.
TL;DR: In this article, experimental observations on the dispersion of fluid in horizontal and vertical tubes where periodic baffles and fluid oscillation may be present were made both at the center and wall of the tube.
Abstract: We report experimental observations on the dispersion of fluid in horizontal and vertical tubes where periodic baffles and fluid oscillation may be present. Local concentration profile measurements are made both at the centre and wall of the tube. Our observations show that small density differences between the tracer and bulk fluid can significantly modify the expected concentration profiles for unbaffled tubes. When baffles and oscillations are present excellent mixing is achieved across the tube and dispersion data are presented for this type of flow.
TL;DR: In this article, the influence of operating conditions, particle properties and bed diameters on radial voidage profiles in circulating fluidized beds operating in the fast regime has been investigated in gas-solid systems.
Abstract: A previously developed method for calibrating an optical-fibre probe for voidage measurement in gas-solid systems has been improved. This was applied to study the influence of operating conditions, particle properties and bed diameters on radial voidage profiles in circulating fluidized beds operating in the fast regime. The present experimental results showed that the radial voidage profile depends solely on the value of the cross-section-averaged voidage, irrespective of operating conditions, solids properties and bed diameters, and can be correlated by the expression epsilon = epsilon-BAR(0.191 + phi-2.5 + 3-phi-11, where epsilon and epsilon-BAR represent the local and cross-section-averaged voidage respectively, and phi-denotes the dimensionless radial distance from the centre of the bed.
TL;DR: In this paper, the Navier-Stokes system is used to estimate the thickness variations over distances long compared to the mean film thickness, and augmented with conjoinging pressure.
Abstract: Dewetting of a solid surface covered by a film of nonwetting liquid either proceeds from a pre-existing dry patch or edge, or initiates from some film-thinning disturbance that cotinues to grow until the film ruptures. Local thinning can be caused by evaporation; by drainage due to gravity or capillarity-driven flow, especially from sharp surfaces; or by surface tension gradients, such as are caused by surface-active substances delivered by particles falling on the film. Once a nonwetting film has been sufficiently thinned, conjoining (negative disjoining) pressure can accelerate thinning until rupture. This catastrophic rupture is modeled here by solving the Navier—Stokes system approximated for thickness variations over distances long compared to the mean film thickness, and augmented with conjoinging pressure. Rupture leads to film retraction and formation of a dry patch. These phenomena are visualized with the aid of moire topography. Of special interest are local spreading disturbances where airborne particles fall on the film surface: craters or dry patches often nucleate. Implications for coating operations are discussed.
TL;DR: In this article, a modified UNIQUAC equation with concentration dependent parameters was used for correlation and prediction of salt effects on vapor-liquid equilibria (VLE) of mixed solvents.
Abstract: The Sander model for correlation and prediction of salt effects on vapor—liquid equilibria (VLE) of mixed solvents combines a term of the Debye—Huckel type with a modified UNIQUAC equation with concentration dependent parameters. In this work the UNIQUAC equation has been substituted by the original UNIFAC group-contribution model with concentration independent group interaction para-meters. Group interaction parameters have been estimated between ions (Li+, Na+, K+, Ca2+, Ba2+, Sr2+, Cu2+, Ni2+, Hg2+, F−, Cl−, Br−, J−, NO3− and CH3COO−), and solvent groups (CH2, OH, CH3OH, H2O, CH3CO), while previously published group interaction parameters between solvent groups have been maintained. It is shwon that the proposed model represents VLE for solvent—water—salt mixtures with an expected average accuracy of the total pressure around 9% and of the vapor-phase mole fractions around 4%. Since it is a predictive group-contribution method it has a much broader range of applicability than the Sander model.
TL;DR: In this article, the authors examined the rate of bubble breakage in turbulent liquid flow using a population balance containing a bubble-breakage model to analyze experimental burstage rate data.
Abstract: The rate of bubble breakage in turbulent liquid flow was examined using a population balance containing a bubble breakage model to analyze experimental bubble breakage rate data. The bubble breakage model was based on high-speed motion photography observations of the breakage process in turbulent liquid pipeline flow. The bubble breakage model predicts the number of bubbles formed from a breakage, the size of the bubbles formed and the rate of bubble breakage. Bubble breakage was determined to be binary; bubble breakage size was described by a breakage size function in which unequal bubble sizes had a higher probability of being formed compared to equal bubble sizes; and the breakage rate was assumed to be first order with respect to the number of bubbles of a given size. The value of the breakage rate constant was found to be approximately equal to the frequency of the second mode of oscillation of the maximum stable bubble size in a given turbulent flow.
TL;DR: In this paper, a mixed integer nonlinear programming (MINLP) formulation is presented for the synthesis of isothermal separator-recycle systems with a variety of objectives such as the minimization of the total annual cost of the plant and the maximization of its profit, as well as objectives traditionally used for optimizing the performance of a reactor network.
Abstract: A systematic synthesis approach is presented for isothermal reactor—separator—recycle systems. The approach proposes a general superstructure of different reactors and separation tasks and features all the potential interconnections among the proposed units. The synthesis problem based upon the proposed superstructure results in a mixed integer nonlinear programming (MINLP) formulation in which the objective function involves both integer and continuous variables and is subject to a nonlinear set of constraints. A variety of objectives was selected for the synthesis problem such as the minimization of the total annual cost of the plant and the maximization of its profit, as well as objectives traditionally used for optimizing the performance of a reactor network such as the product yield and selectivity. Discussion of the results and comparison among the different solutions obtained provided the ground for conclusions related to the potential trade-offs and the performance of the isothermal chemical systems under consideration.
TL;DR: In this paper, the formation and growth of cakes in cake filtration taking into account of cake compression and the moving-boundary nature of the growth process are derived and methods for their solutions developed.
Abstract: Equations describing the formation and growth of cakes in cake filtration taking into account of cake compression and the moving-boundary nature of the growth process are derived and methods for their solutions developed. The numerical solutions provide detailed information about cake growth including the cake thickness and its structure as functions of time. Comparisons between the present analysis and conventional cake filtration theories are presented.
TL;DR: In this paper, a Monte Carlo computer simulation model for a class of particle transport processes in flow through a porous medium is developed, which includes transport of macromolecules in porous media, fines migration, flow of stable emulsion, deep-bed filtration and size-exclusion chromatography.
Abstract: In this paper we develop a Monte Carlo computer simulation model for a class of particle transport processes in flow through a porous medium. This class of problems includes transport of macromolecules in porous media, fines migration, flow of stable emulsion, deep-bed filtration and size-exclusion chromatography. The porous medium is represented by a three-dimensional network of interconnected cylindrical pores with nonuniform (possibly fractal) surfaces. The effective radii of the pores are distributed according to an experimentally-measured pore size distribution. The paths of the particles throughout the pore space are determined rigorously, taking into account the effect of various forces that contribute to the interaction of the particles with the pore space. The model can also take into account the effect of possible pore plugging, particle deposition and macromolecular adsorption on the surface of the pores, in which case such phenomena are percolation processes and are characterized by a percolation threshold which is the volume fraction of the open pores below which the medium loses its macroscopic connectivity. When the model is applied to the problem of fines migration in flow through a porous medium, the predictions are in quantitative agreement with the available experimental data.
TL;DR: In this paper, the results of detailed numerical simulations using such a model for the flow generated by a downflow-pitched blade turbine in a fully baffled cylindrical vessel and the subsequent bulk mixing are described.
Abstract: A flow and mixing model can provide a sound fundamental basis for the quantitative and optimum design of impeller and tank geometries. This paper describes the results of detailed numerical simulations using such a model for the flow generated by a downflow-pitched blade turbine in a fully baffled cylindrical vessel and the subsequent bulk mixing. Comparisons of predicted flow characteristics with experimental data (measured in a 0.3 m i.d. vessel using a laser Doppler anemometer) show good agreement. The results of this flow model were then used to simulate the mixing of an inert tracer (introduced in pulse mode) in agitated tanks. Various mixing time definitions were studied and compared with published correlations. Some numerical experiments were performed to generate guidelines for the development of new impellers.
TL;DR: In this article, the radial porosity model is correlated in terms of the diameter aspect ratio and a non-dimensional distance from the container wall, which can be used in analytical transport models for simulating packed beds of uniform spheres in cylindrical containers.
Abstract: The purpose of the investigation is to correlate the experimental data of Roblee et al. (1958) Brosilow (1959), Benenati and Brosilow (1962) and Ridgway and Tarbuck (1966) to produce an empirical model which consists of one principal equation for the radial porosity distribution and includes the damped oscillations. The radial porosity model is correlated in terms of the diameter aspect ratio and a non dimensional distance from the container wall. The model can be used in analytical transport models for simulating packed beds of uniform spheres in cylindrical containers
TL;DR: In this paper, numerically generated flow visualisation simulations for the flow of an incompressible Newtonian fluid within a two-dimensional channel which can contain periodic baffles are presented.
Abstract: We report numerically generated flow visualisation simulations for the flow of an incompressible Newtonian fluid within a two-dimensional channel which can contain periodic baffles. For unsteady flows in this geometry a regime of chaotic advection is observed when baffles are present. The unsteadiness takes one of two forms: a “natural” unsteadiness caused by a symmetry breaking instability of the flow, or a “forced” unsteadiness generated by applying an oscillatory component to the flow. This chaotic advection is shown to provide an efficient mixing mechanism and has a number of applications in the process industry. Enhanced transverse mixing is observed which results in increased transfer properties, reduced fouling rates and, in some circumstances, a reduction in axial dispersion, as recently experimentally reported in the literature.
TL;DR: In this paper, an experimental study of the axial segregation process for particle mixture of different sizes is presented. And a mechanism for the segregation process is presented based on which criteria for axial separation are discussed.
Abstract: We report on an experimental study of the axial segregation process for particle mixture of different sizes. The effect of particle volume fraction and rotational speed on band formation is considered. A mechanism for the segregation process is presented based on which criteria for axial segregation are discussed
TL;DR: In this paper, the authors show how intraparticle convection affects residence time distribution of inert and linearly adsorbed species in fixed-bed processes and demonstrate how column efficiency is improved by the use of large-pore supports.
Abstract: Large-pore materials are used in various chemical engineering applications as catalysts, HPLC packings, ceramic membranes. In such supports, mass transfer due to intraparticle convection has to be taken into account. This paper shows how intraparticle convection affects residence time distribution of inert and linearly adsorbed species in fixed-bed processes. The concept is further illustrated with examples from gas—solid systems and liquid—solid systems (HPLC) showing how the column efficiency (measured by HETP in separation engineering) is improved by the use of large-pore supports.
TL;DR: In this paper, an expression relying on fluid mechanical and phenomenological considerations is proposed for the agglomeration rate of adipic acid crystals during their crystallization in a mechanically stirred crystallizer.
Abstract: An expression relying on fluid mechanical and phenomenological considerations is proposed for the agglomeration rate of adipic acid crystals during their crystallization in a mechanically stirred crystallizer. This expression accounts for the influence of particle concentration, supersaturation, power dissipation per unit mass, size of crystallizer and size of agglomerating crystals. The formation is adapted to the discretization method of the CSD into granulometric classes which was presented in a previous paper of this series. It is shown that crystal size strongly influences the agglomeration rate. The model involves one single free parameter for the agglomeration rate and can easily be applied to other agglomeration processes occurring in the supermicronic range during crystallization.
TL;DR: In this paper, a mathematical description for a flowing mixture of solid particulates and a fluid is developed within the context of mixture theory, and the equations governing the flow of a two-component mixture of a Newtonian fluid and a granular solid are derived.
Abstract: A mathematical description for a flowing mixture of solid particulates and a fluid is developed within the context of mixture theory. Specifically, the equations governing the flow of a two-component mixture of a Newtonian fluid and a granular solid are derived. These relatively general equations are then reduced to a system of coupled ordinary differential equations describing a steady flow of the mixture between flat plates. The resulting boundary value problem is solved numerically and results are presented for cases in which drag and lift interactions are important.
TL;DR: In this article, the hydrodynamic response of a small suspended sphere to laminar flow is studied for relatively fast flow rates in a duct with porous walls, and an expression is developed, from first principles, to predict conditions under which a sufficiently long cross-flow plate and frame membrane module exposed to dilute suspensions of essentially spherical particles will not foul, assuming nonhydrodynamic attractions between a particle and the membrane are negligible.
Abstract: The hydrodynamic response of a small suspended sphere to laminar flow is studied for relatively fast flow rates in a duct with porous walls. There is a lift effect on the sphere which competes with a wall suction effect. The details of this balance determine whether the sphere will reach the membrane. An expression is developed, from first principles, to predict conditions under which a sufficiently long cross-flow plate and frame membrane module exposed to dilute suspensions of essentially spherical particles will not foul, assuming nonhydrodynamic attractions between a particle and the membrane are negligible. This is the first expression which might be properly tested experimentally to determine if the elevated permeation rates observed with colloidal suspensions (Porter, 1972) are due to particle lift or to some other phenomena such as a flowing cake. The strongest particle lift effect occurs when the sphere is much closer to one wall than the other and is due to convective interaction of the disturbance caused by the sphere and the undisturbed flow, in the presence of the nearby wall. The lift velocity has the same dependence on parameters as the previous results derived for slow laminar flow (Cox and Brenner, 1968; Ho and Leal, 1974). However, the maximum lift velocity is smaller than that found by Vasseur and Cox (1976) by roughly a factor of 2.6. These results agree with those of Schonberg and Hinch (1989) in the following features: the equilibrium position moves with increasing Reynolds number towards the wall, the magnitude of the velocity near the wall is in good agreement, and our results extend to higher Reynolds number. Also, the results are compared with the experiments of Segre and Silberberg (1962a, b).
TL;DR: In this article, the Patel-Teja equation of state (PT EOS) is extended to phase equilibrium calcultations for electrolyte solutions under high pressure by adding a Debye-Huckel electrostatic contribution term.
Abstract: The Patel—Teja equation of state (PT EOS) is extended to phase equilibrium calcultations for electrolyte solutions under high pressure by adding a Debye—Huckel electrostatic contribution term A new mixing rule similar to that developed by Kurihara (1987) is used for the energy parameter a The extended PT EOS retains its original cubic form in volume The binary interaction parameters are determined: for water—salt pairs (from osmotic coefficient data of aqueous solutions at 25°C); for gas—water pairs (from VLE data of binary nonelectrolyte mixtures); and for salt—gas pairs (from low-pressure gas solubility data in aqueous salt solutions) Satisfactory results are obtained
TL;DR: In this paper, the authors investigated the low-pressure methanol synthesis over Polish commercial catalyst CuO (60% wt), ZnO (30%) and Al 2 O 3 (7.5%).
Abstract: Kinetics of the low-pressure methanol synthesis over Polish commercial catalyst CuO (60% wt)—ZnO (30%)—Al 2 O 3 (7.5%) was investigated. The range of parameters applied was wide, especially concerning inlet concentrations of reactants: χ H 2 0 (10–80% mol), χ CO 2 0 (3–40% mol), χ CO 0 (0–20% mol). It was found that methanol synthesis occurs from CO 2 rather than from CO and that the basic reactions are: CO 2 +3H 2 ⇄CH 3 OH+H 2 O and CO 2 +H 2 ⇄CO+H 2 O. Dependence of the reaction rates on initial concentrations of CO 2 and H 2 was given by the functions with characteristic maxima. Langmuir-Hinshelwood type kinetic equations were determined.
TL;DR: In this article, a new approach for calculating minimum flows in simple distillation columns is presented, which is suited for the evaluation of a large number of distillation sequences in terms of energy consumption at early stages of process design.
Abstract: A new approach for calculating minimum flows in simple distillation columns is presented. Unlike most previous work, no assumptions concerning ideal boiling or enthalpy behavior are required. The computation time is low, because neither rigorous simulation runs nor column iteration procedures are involved, and the method is suited for the evaluation of a large number of distillation sequences in terms of energy consumption at early stages of process design. The basic idea is the description of a distillation column under minimum reflux conditions by means of the reversible distillation model, which will be introduced briefly. The new method has been applied successfully to nonideal and azeotropic systems. Several calculations are illustrated with comparisons both to a rigorous and to the Underwood method. It will also be explained and demonstrated that the prediction and determination of tangent pinch points is a logical extension of the reversible distillation model.