AICHE Journal
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Solvent extraction with microporous hydrophilic and composite membranes Abstract Dispersion‐free solvent extraction using microporous hydrophobic membranes has been extended to hydrophilic and composite hydrophobic‐hydrophilic membranes. Excess phase pressure conditions, if needed for dispersion‐free operation, have been identified. Boundary layer and membrane resistances to solute transport have been isolated and simple relations developed for the overall mass transfer coefficient in such systems. A variety of flat microporous membranes have been utilized. Previous investigations by others had interpreted the membrane mass transfer resistance using the notion of unhindered diffusion through tortuous pores of the membrane. We have studied here the applicability and limitations of such a model for a number of membrane‐solute‐solvent systems.
AICHE Journal - Tập 33 Số 7 - Trang 1057-1066 - 1987
An analytical study of laminar counterflow double‐pipe heat exchangers Abstract An orthogonal expansion technique for solving a new class of counterflow heat transfer problems is developed and applied to the detailed study of laminar flow concentric tube heat exchangers. The exchanger problem is solved for fully developed laminar velocity profiles, negligible longitudinal conduction in the fluid streams and in the exchanger walls, and with fluid properties which are independent of the temperature. A description of the variation of the local Nusselt numbers and the temperature at the wall between the two streams is given. Also reported are bulk temperature changes in the two streams and mean overall Nusselt numbers. It is shown that for long exchangers, which are of some industrial importance, asymptotic Nusselt numbers exist in counterflow as in single‐phase and cocurrent systems. Numerical values of asymptotic Nusselt numbers are reported for a wide range of parameters. Comparisons are made with single‐stream solutions such as the Graetz problem, with empirical correlations of experimental data, and with cocurrent flow exchangers. To solve this problem it was necessary to derive new orthogonality relations, and also expressions for determining positive and negative sets of eigenvalues and eigenvectors. Satisfaction of inlet boundary conditions at both ends of counterflow exchangers requires a complete set of eigenfunctions and thus one must use both the positive and negative sets.
AICHE Journal - Tập 12 Số 2 - Trang 279-289 - 1966
Fractional extraction with hollow fibers with hydrogel‐filled walls Abstract Extractions using hollow fibers can be faster and more efficient than those in conventional equipment. These advantages, due to the large area per volume possible with fibers, can be compromised by accidental convection through the fibers' pores. When these pores are filled with gels of crosslinked polyvinyl alcohol, convection through the pores is stopped but the overall mass transfer is unaltered. The separations across these gel‐filled fiber walls provide excellent yield and purity, especially in the case of fractional extraction.
AICHE Journal - Tập 37 Số 6 - Trang 855-862 - 1991
A theoretically correct mixing rule for cubic equations of state Abstract A new mixing rule developed for cubic equations of state equates the excess Helmholtz free energy at infinite pressure from an equation of state to that from an activity coefficient model. Use of the Helmholtz free energy insures that the second virial coefficient calculated from the equation of state has a quadratic composition dependence, as required by statistical mechanics. Consequently, this mixing rule produces the correct low‐ and high‐density limits without being density‐dependent. As a test, the mixing rule is used for ternary mixtures of cyclohexane + benzene + water, ethanol + benzene + water and carbon dioxide + n‐propane + water, and all the constituent binaries. The new mixing rule and a simple cubic equation of state can be used for the accurate correlation of vapor‐liquid and liquid‐liquid equilibria for binary mixtures. Using the parameters obtained from binary systems, the phase behavior of ternary mixtures can be predicted. Also, unlike previous empirical mixing rules, this theoretically based mixing rule is equally applicable and accurate for simple mixtures containing hydrocarbons and inorganic gases and mixtures containing polar, aromatic and associating species over a wide range of pressures. This mixing rule makes it possible to use a single equation of state model with equal accuracy for mixtures usually described by equations of state and for those traditionally described by activity coefficient models. It is the correct bridge between these two classes of models.
AICHE Journal - Tập 38 Số 5 - Trang 671-680 - 1992
Dispersion‐free solvent extraction with microporous hollow‐fiber modules Abstract Extensive studies on dispersion‐free solvent extraction have been carried out using modules made with either hydrophobic or hydrophilic microporous hollow‐fiber membranes. Membrane and boundary layer resistances have been characterized for both kinds of hollow fiber using solvent extraction systems with a wide variation of distribution coefficients and interfacial tensions. It has been found that the Graetz solution for a constant wall concentration describes satisfactorily mass transfer on the lumen side of a hollow‐fiber device. A correlation of the form N Sh D h L ]N N
AICHE Journal - Tập 34 Số 2 - Trang 177-188 - 1988
Effective and coupled thermal conductivities of isotropic open‐cellular foams Abstract The effective and the coupled thermal conductivity of the solid microstructure of open‐cellular foams and an accompanying saturation fluid are defined in a conceptual representation of conductive heat transfer in a two‐phase system of which the phases are in a thermal nonequilibrium state. The effective and coupled thermal conductivities were determined from a close observation of the relationship between microscopic and macroscopic temperature distributions. Temperature distributions were obtained from the numerical solution of the three‐dimensional (3‐D) conduction equation in a representative geometrical model of the foam solid microstructure and the fluid pores. Empirical correlations are provided for the effective and coupled thermal conductivities in terms of the solid and the fluid thermal conductivity and foam porosity. Thermal radiation was not considered in the energy transfer process. © 2004 American Institute of Chemical Engineers AIChE J, 50: 547–556, 2004
AICHE Journal - Tập 50 Số 3 - Trang 547-556 - 2004
Steady‐state and transient analysis of a CH<sub>4</sub>–catalytic partial oxidation reformer Abstract In this work dynamic and steady‐state CH4 partial oxidation tests, performed in an insulated lab‐scale reactor over a Rh‐based catalyst supported onto Al2 O3 spheres, are presented and discussed. To gain insight in the complex observed phenomena a previously developed 1D heterogeneous mathematical model of adiabatic reactor was applied to data analysis. The model implemented an indirect reaction scheme independently derived in previous works. In experiments at low flow rates the heat dispersion significantly affected the steady‐state response of the reactor; the process was governed by thermodynamics. By increasing the flow rate the catalytic bed progressively heated up and the adiabatic behavior was approached as a result of the predominance of the reaction enthalpy release over the heat losses; a kinetic effect of contact time was observed. Under these conditions start‐up dynamics of the process were acquired. The temporal evolution of the product distribution along with the shape of axial temperature profiles at steady state were consistent with the occurrence of an indirect reaction path leading to the formation of synthesis gas. A sensitivity analysis showed that the description of the temperature profiles and conversion/selectivity performances at steady state is greatly influenced by the rate of the reforming reactions; the simulation of the reactor start‐up dynamics is highly sensitive to the initial solid temperature. The comparison between measured temperature profiles and model predictions suggested that the thermocouple measurements were mainly influenced by the temperature of the flowing gas. © 2006 American Institute of Chemical Engineers AIChE J, 2006
AICHE Journal - Tập 52 Số 9 - Trang 3234-3245 - 2006
Modeling the partial oxidation of methane in a short‐contact‐time reactor Abstract Partial oxidation of methane in monolithic catalysts at very short contact times offers a promising route to convert natural gas into syngas (H2 and CO), which can then be converted to higher alkanes or methanol. Detailed modeling is needed to understand their complex interaction of transport and kinetics in these systems and for their industrial application. In this work, the partial oxidation of methane in noble‐metal (Rh and Pt)‐coated monoliths was studied numerically as an example of short‐contact‐time reactor modeling. A tube wall catalytic reactor was simulated as a model for a single pore of the monolithic catalyst using a 2‐D flow field description coupled with detailed reaction mechanisms for surface and gas‐phase chemistry. The catalytic surface coverages of adsorbed species are calculated vs. position. The reactor is characterized by competition between complete and partial oxidation of methane. At atmospheric pressure, CO2 and H2 O are formed on the catalytic surface at the entrance of the catalytic reactor. At higher pressure, gas‐phase chemistry becomes important, forming more complete oxidation products downstream and decreasing syngas selectivity by about 2% at 10 bar. Temperature (from 300 to ∼ 1,200 K), velocity, and transport coefficients change very rapidly at the catalyst entrance. The dependence of conversion and selectivity on reactor conditions was examined.
AICHE Journal - Tập 44 Số 11 - Trang 2465-2477 - 1998
Steps in CH<sub>4</sub> oxidation on Pt and Rh surfaces: High‐temperature reactor simulations Abstract The direct oxidation of CH4 to H2 and CO in O2 and in air at high temperatures over alumina foam monoliths coated with high loadings of Pt and Rh has been simulated using a 19‐elementary‐step model of adsorption, desorption and surface reaction steps with reaction parameters from the literature or from fits to previous experiments. The surface reaction model for Pt is in good agreement with previously reported low‐pressure(0.1 to 1 torr) reactor measurements of CH4 oxidation rates at temperatures from 600 to 1,500 K and of OH radical desorption during CH4 oxidation at 1,300 to 1,600 K over polycrystalline Pt foils. The model predictions for both catalysts are also consistent with product selectivities observed over monolithic catalysts in an atmospheric‐pressure laboratory‐scale reactor, and the differences between Pt and Rh can be explained by comparing individual reaction steps on these surfaces. Because of the good agreement between the model and both low‐and atmospheric‐pressure reactor simulations, a complete energy diagram for methane oxidation at low coverages is proposed. The model results show that under CH4 rich conditions at high temperatures, H2 and CO are primary products of the direct oxidation of methane via a pyrolysis mechanism.
AICHE Journal - Tập 39 Số 7 - Trang 1164-1177 - 1993
A C<sub>1</sub> microkinetic model for methane conversion to syngas on Rh/Al<sub>2</sub>O<sub>3</sub> Abstract A microkinetic model capable of describing multiple processes related to the conversion of natural gas to syngas and hydrogen on Rh is derived. The parameters of microkinetic models are subject to (intrinsic) uncertainty arising from estimation. It is shown that intrinsic uncertainty could markedly affect even qualitative model predictions (e.g., the rate‐determining step). In order to render kinetic models predictive, we propose a hierarchical, data‐driven methodology, where microkinetic model analysis is combined with a comprehensive, kinetically relevant set of nearly isothermal experimental data. The new, thermodynamically consistent model is capable of predicting several processes, including methane steam and dry reforming, catalytic partial oxidation, H2 and CO rich combustion, water‐gas shift and its reverse at different temperatures, space velocities, compositions and reactant dilutions, using the measured Rh dispersion as an input. Comparison with other microkinetic models is undertaken. Finally, an uncertainty analysis assesses the effect of intrinsic uncertainty and catalyst heterogeneity on the overall model predictions. © 2009 American Institute of Chemical Engineers AIChE J, 2009
AICHE Journal - Tập 55 Số 4 - Trang 993-1008 - 2009
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