Showing papers in "Aiche Journal in 1998"
TL;DR: Multiscale Principal Component Analysis (MSPCA) as mentioned in this paper combines the ability of PCA to decorrelate the variables by extracting a linear relationship with that of wavelet analysis to extract deterministic features and approximately decorrelation of autocorrelated measurements.
Abstract: Multiscale principal-component analysis (MSPCA) combines the ability of PCA to decorrelate the variables by extracting a linear relationship with that of wavelet analysis to extract deterministic features and approximately decorrelate autocorrelated measurements. MSPCA computes the PCA of wavelet coefficients at each scale and then combines the results at relevant scales. Due to its multiscale nature, MSPCA is appropriate for the modeling of data containing contributions from events whose behavior changes over time and frequency. Process monitoring by MSPCA involves combining only those scales where significant events are detected, and is equivalent to adaptively filtering the scores and residuals, and adjusting the detection limits for easiest detection of deterministic changes in the measurements. Approximate decorrelation of wavelet coefficients also makes MSPCA effective for monitoring autocorrelated measurements without matrix augmentation or time-series modeling. In addition to improving the ability to detect deterministic changes, monitoring by MSPCA also simultaneously extracts those features that represent abnormal operation. The superior performance of MSPCA for process monitoring is illustrated by several examples.
812 citations
TL;DR: In this paper, a 2D mathematical model for the entire sandwich of a proton-exchange membrane fuel cell including the gas channels was developed, where a self-consistent model for porous media was used for the equations describing transport phenomena in the membrane, catalyst layers, and gas diffusers, while standard equations of Navier-Stokes, energy transport, continuity, and species concentrations are solved in the gas channel.
Abstract: A 2-D mathematical model for the entire sandwich of a proton-exchange membrane fuel cell including the gas channels was developed The self-consistent model for porous media was used for the equations describing transport phenomena in the membrane, catalyst layers, and gas diffusers, while standard equations of Navier-Stokes, energy transport, continuity, and species concentrations are solved in the gas channels A special handling of the transport equations enabled us to use the same numerical method in the unified domain consisting of the gas channels, gas diffusers, catalyst layers and membrane It also eliminated the need to prescribe arbitrary or approximate boundary conditions at the interfaces between different parts of the fuel cell sandwich By solving transport equations, as well as the equations for electrochemical reactions and current density with the membrane phase potential, polarization curves under various operating conditions were obtained Modeling results compare very well with experimental results from the literature Oxygen and water vapor mole fraction distributions in the coupled cathode gas channel-gas diffuser were studied for various operating current densities Liquid water velocity distributions in the membrane and influences of various parameters on the cell performance were also obtained
595 citations
TL;DR: The Damkohler number is shown to dictate the type of wormhole structure formed by systems with various degrees of transport and reaction limitations, and results from a 2-D network model and a 3-D physically representative network model agree qualitatively with experimental results and substantiate the existence of an optimum Damk Kohler number.
Abstract: The transport and reaction of fluids in porous media results in unique pore growth and channel evolution as the media are dissolved. This often leads to the formation of highly conductive flow channels, commonly referred to as wormholes. The objective of this work is to predict the influence of transport and reaction on the structure of the wormhole channels. An experimental and theoretical investigation of a variety of fluid systems, including strong acids, weak acids, and chelating agents, provides a wide range of conditions for studying wormhole formation. A generalized description of the dissolution phenomenon is introduced, and a common dependence on the Damkohler number is demonstrated. The Damkohler number is shown to dictate the type of wormhole structure formed by systems with various degrees of transport and reaction limitations. An optimum Damkohler number for channel formation is observed at a value of approximately 0.29 for all of the fluid systems investigated. The stochastic nature of the dissolution phenomenon is described using network models. Results from a 2-D network model and a 3-D physically representative network model agree qualitatively with experimental results and substantiate the existence of an optimum Damkohler number.
460 citations
TL;DR: In this article, the application of dynamic time warping (DTW) to the analysis and monitoring of batch processes is presented, which has the ability to synchronize two trajectories by appropriately translating, expanding, and contracting localized segments within both trajectories to achieve a minimum distance between the trajectories.
Abstract: The application of dynamic time warping (DTW) to the analysis and monitoring of batch processes is presented. This dynamic-programming-based technique has been used in the area of speech recognition for the recognition of isolated and connected words. DTW has the ability to synchronize two trajectories by appropriately translating, expanding, and contracting localized segments within both trajectories to achieve a minimum distance between the trajectories. Batch processes often are characterized by unsynchronized trajectories, due to the presence of batch-to-batch disturbances and the existence of physical constraints. To compare these batch histories and apply statistical analysis one needs to reconcile the timing differences among these trajectories. This can be achieved using DTW with only a minimal amount of process knowledge. The combination of DTW and a monitoring method based on Multiway PCA/PLS is used for both off-line and on-line implementation. Data fiom an industrial polymerization reactor are used to illustrate the implementation and the performance of this method.
449 citations
TL;DR: In this paper, the fundamental issues of detectability, reconstructability, and isolatability for multidimensional faults are studied using principal component analysis (PCA) and partial least squares.
Abstract: Fault detection and process monitoring using principal-component analysis (PCA) and partial least squares were studied intensively and applied to industrial processes. The fundamental issues of detectability, reconstructability, and isolatability for multidimensional faults are studied. PCA is used to define an orthogonal partition of the measurement space into two orthogonal subspaces, a principal-component subspace, and a residual subspace. Each multidimensional fault is also described by a subspace on which the fault displacement occurs. Fault reconstruction leads to fault identification and consists of finding a new vector in the fault subspace with minimum distance to the principal-component subspace. The unreconstructed variance is proposed to measure the reliability of the reconstruction procedure and determine the PCA model for best reconstruction. Based on the fault subspace, fault magnitude, and the squared prediction error, necessary and sufficient conditions are provided to determine if the faults are detectable, reconstructable, and isolatable.
381 citations
TL;DR: In this article, a defect-free Pd membrane was prepared by an electroless plating technique on porous stainless-steel tubes and the effective surface of Pd membranes was up to 75 cm2.
Abstract: Defect-free Pd membranes were prepared by an electroless plating technique on porous stainless-steel tubes. The effective surface of Pd membranes was up to 75 cm2. The helium flux was not detected at room temperature and pressure difference of 3 atm. At 350°C hydrogen permeances of up to were obtained. A t a pressure difference of 1 atm and 350°C, selectivity coefficients as high as J(H2/JN2) = 5,000 were observed. Fluxes of gases, impermeable through the Pd, were quantitatively described as a combination of Knudsen diffusion and viscous flow through the gaps created in the Pd layer at high temperatures. The stability of the prepared membranes at temperatures up to 700°C was investigated. The membranes were stable at 350°C over a period of 1,100 h, with no significant changes in the steady-state hydrogen flux and with a recrystallization texture and aggregation of Pd grains.
326 citations
TL;DR: In this article, the formation of calcite, aragonite, and vatente is investigated using a constant-composition method, and three polymorphs are produced. But the effects of the additive are complicated depending on its fype and concentration as well as the operating conditions.
Abstract: Polymorphism of calcium carbonate was investigated using a constant-composition method, and three polymorphs- calcite, aragonite, and vatente- are produced. Factors that affect the formation of polymorphs are studied over a wide range, including solution pH, temperature, concentration ratio of components, supersaturation, ionic strength, and fype and concentration of additives. At room temperature, solution pH is the most significant factor, and high yield polymorphs are present at different pH values. At a high temperature, aragonite becomes the major product at a pH below 12. The effects of the additive are complicated, depending on its fype and concentration as well as the operating conditions. The influence of concentration ratio and supersaturation on the formation of po[ymorphs is less significant, Besides, uarious particle morphologies of CaCO, polymorphs are observed, depending on the operating conditions.
303 citations
TL;DR: Proportional integral, and derivative (PID) parameters are obtained for general process models by approximating the feedback form of an IMC controller with a Maclaurin series in the Laplace variable.
Abstract: Proportional integral, and derivative (PID) parameters are obtained for general process models by approximating the feedback form of an IMC controller with a Maclaurin series in the Laplace variable. These PID parameters yield closed-loop responses that are closer to the desired responses than those obtained by PID controllers tuned by other methods. The improvement in closed-loop control performance becomes more prominent as the dead time of the process model increases. A new design method for two degree of freedom controllers is also proposed. Such controllers are essential for unstable processes and provide significantly improved dynamic performance over single degree of freedom controllers for stable processes when the disturbances enter through the process.
295 citations
TL;DR: In this paper, a regime map of granule growth behavior is proposed based on granule deformation during collision and the granule liquid content measured as the maximum pore saturation.
Abstract: A regime map of granule growth behavior is proposed based on granule deformation during collision and the granule liquid content measured as the maximum pore saturation. The granule deformability on collision is represented by a deformation number, which is a ratio of granule impact energy to the plastic energy absorbed per unit strain. Granule growth regimes such as steady growth, induction, nudeation, crumb, and slurry are defined. Ttus regime map qualitatively explains the variations in granulation behavior. Laboratory drum granulation experiments were used to test the regime map. Experiments were performed in a 0.3-m-dia. drum using three sizes of glass ballotini (19, 31, and 60 μm) with water andglycerol as liquid binders. Increasing granule yield stress by decreasing particle size and increasing binder viscosity caused the system to move from steady growth to induction behavior as predicted by the regime map. Preliminary validation with literature data was also encouraging. More work, however, is required to better quantify the boundaries bet\veen different growth regimes and to investigate the effect of process agitation intensity. Tfiis regime map has great potential to help design and control granulation systems, because it is based on properties of the powder/binder system that can be measured or estimated without performing any granulation tests.
269 citations
TL;DR: In this paper, a front of close-packed particles is predicted for both infinite and finite domains as a function of the maximum capillary pressure, and the positions of the front are predicted for different size areas.
Abstract: Latex films cast on a substrate often dry nonuniformly, with a drying front separating fluid domains from solidified regions passing across the film. For initial film thicknesses that are smaller than the characteristic horizontal distance, the analysis predicts surface-tension-driven horizontal flow. In a limit that ensures vertical homogeneity it is shown how a front of close-packed particles forms and propagates. Imposing a maximum for the capillary pressure causes a solvent front to recede into the film. This recession is minimal, but can markedly affect the propagation of the particle front. An overall mass balance offers a solution for infinite capillary pressure, thereby illustrating the mechanism for propagation of the front. The positions of the fronts are predicted for both infinite and finite domains as a function of the maximum capillary pressure. Selective or nonuniform evaporation produces final film profiles, while the evaporating regions are still visible. After predictions over different size areas are made, the smallest area is compared with experiment.
260 citations
TL;DR: In this paper, 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.
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 H2O 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.
TL;DR: In this paper, superficial velocity profiles inside a packed bed were obtained for monodisperse packings of spheres, deformed spheres, cylinders and Raschig-ring by averaging over several thousand local measurements of the axial flow components within a cross-section.
Abstract: For liquid flow, superficial velocity profiles inside a packed bed were obtained for monodisperse packings of spheres, deformed spheres, cylinders and Raschig-ring by averaging over several thousand local measurements of the axial flow components within a cross-section. At fully developed flow, the profiles are constant along the packing except for short inlet and outlet zones of about three particles layer length with either a buildup of the profile at the inlet or a degeneration at the exit of the packed bed. Besides velocity profiles, porosity distribution functions were also evaluated experimentally. These were introduced in the extended Brinkman equation which simulates the fluctuating profiles well if the average porosity of the packing is replaced by the radial porosity distribution. The effective viscosity is adjusted to obtain best agreement between measurements and solutions of the Brinkman equation. This effective property, however, influences the flow profile in the very near wall range only, up to approximately a distance of about half the particle diameter. The effective viscosity is found to depend on the porosity data close to the wall, on particle shape, on the Reynolds number, and on the pressure loss relation.
TL;DR: In this article, the effect of water on the two decomposition pathways and on the isomerization of formic acid was determined, and it was shown that water acts as a homogeneous catalyst for both dehydration and decarboxylation.
Abstract: Formic acid decomposes primarily to CO and H2 0 in the gas phase, but to CO, and H, in the aqueous phase. Ab-initio quantum chemical calculations were performed, using Hartree-Fock and density functional methods, to seek an explanation for this behavior. The effect of water on the two decomposition pathways and on the isomerization of formic acid was determined. The transition state structures were fully optimized and include up to two water molecules. In the absence of water, dehydration is more favorable than decarboxylation. The presence of water reduces the activation barriers for both decomposition pathways, but decarboxylation is consistently more favorable than dehydration. The water molecules actively participate in the bond-breaking and bondforming processes in the transition state. The reduction in the activation barriers with the addition of water indicates that water acts as a homogeneous catalyst for both dehydration and decarboxylation, whereas isomerization of formic acid occurs independently of water. Water has a strong effect on the relative stability of the formic acid isomers, acid - water complexes, and transition states. The relative stability of the transition states plays an important role in determining the faster decomposition pathway.
TL;DR: In this paper, a predictive model for the performance of a nanofiltration membrane in separating the components of a dye/salt solution was developed based on the extended Nernst-Planck equation with incorporation of concentration polarization for mixtures of charged ions.
Abstract: A predictive model for the performance of a nanofiltration membrane in separating the components of a dye/salt solution was developed. It is based on the extended Nernst-Planck equation with incorporation of concentration polarization for mixtures of charged ions. Excellent agreement between predicted and experimental rejections of anions and cations was obtained for batch nanofiltration at different ratios of dye/salt assuming that the membrane charge density (Xd) depends on the total concentration of negative charges in the solutions. Prediction for diafiltration experiments was also excellent by allowing for variation in Xd as the salt concentration in the solution changed as a function of time. The model was used to investigate optimization of the processing conditions. The overall diafiltration process operated best in a two-phase mode, in which the dye solution was preconcentrated to the final required dye concentration before diafiltration.
TL;DR: In this paper, a monolayer AgNO3/SiO2 sorbent was used for olefin/parafin separations by pressure-swing adsorption.
Abstract: Monolayer dispersed AgNO3 on silica gel was prepared by thermal dispersion. This sorbent exhibited superior adsorption properties for olefin/parafin separations by selective adsorption of olefins through π-complexation. This sorbent, along with Ag+ ion-exchanged resin, was subjected to simulation studies for olefin/parafin separations by pressure-swing adsorption. Kinetic separations (due to differences in olefin/parafin diffusivities) using zeolite 4A and molecular-sieve carbon were also studied, Using 50/50 mixtures of C2 H4/C2 H6 and C3H6/C3H8, separations using these sorbents were compared directly based on olefin product purity, recoveiy, and throughput. The monolayer AgNO3/SiO2 sorbent showed superior separation results for C3H4/C3H8, and the Ag+-exchanged resin showed best results for C2H4/C2H6. In both cases, over 99% product purities could be obtained at reasonably high recoveries and throughputs. For C3H6/C3H6 separation on AgNO3/SiO2, multiplicity of cyclic steady states were observed within certain regions of feed and purge velocities. within these regions, two stable cyclic steady states were reached starting ffom different initial-bed conditions while all operating conditions were identical.
TL;DR: In this article, the crystal orientation of the MFI films was examined using X-ray diffraction pole-figure texture analysis, showing that the crystals were preferentially oriented with both sinusoidal and straight channel networks along directions nearly parallel to the membrane surface.
Abstract: MFI membranes were prepared as free-standing and supported films on porous alumina disks and nonporous substrates. They were synthesized using secondary growth of precursor layers. For self-supported films the first step was to prepare an alumina–silicalite composite film, while for supported films the substrate was first coated with layers of the nanocrystalline silicalite particles. During the following hydrothermal treatment, silicalite particles acting as seed crystals form a dense film, which consists of 0.5–100-μm-thick columnar, intergrown, preferentially oriented grains. The crystal orientation of the MFI films was examined using X-ray diffraction pole-figure texture analysis. The crystals were preferentially oriented with both sinusoidal and straight channel networks along directions nearly parallel to the membrane surface. The degree of orientation increased with increasing membrane thickness. Single gas permeances through thin, oriented membranes were measured. Apparent actiuation energies for permeation were 16, 24, 30, 22 and 26 kj/mol for H2, N2, O2, CH4, and CO2, respectively. Ideal selectivities for H2/N2, CO2/CH4, and O2/N2 were as high as 30, 10, and 3.5, respectively. Binary permeation measurements for the gas pairs CO2/CH4, O2/N2, and CO2/N2 revealed trends similar to those of single gas permeation and the properties are attributed to the membrane microstructure.
TL;DR: In this article, a model for multicomponent gas separation using hollow-fiber contactors was developed for simulation of cocurrent, countercurrent, and crossflow contacting patterns with permeate purging (or sweep).
Abstract: A model developed for multicomponent gas separation using hollow-fiber contactors permits simulation of cocurrent, countercurrent, and crossflow contacting patterns with permeate purging (or sweep). The numerical approach proposed permits simulation to much higher stage cuts than previously published work and provides rapid and stable solutions for cases with many components, with widely varying permeability coefficients. This new approach also permits the rational and straightforward incorporation of effects such as permeate sweep, pressure-dependent permeability coefficients, and bore side pressure gradients. Simulation results are presented for separation of commercially significant multicomponent gas mixtures using polymer permeation properties similar to those of polysulfone. The effect of permeate purging on separation performance is explored for air separation. The influence of pressure ratio on hydrogen separation performance for a refinery stream is presented. Air is modeled as a four-component mixture of O2, N2, CO2, and H2O and the refinery stream contains five components: H2, CH4, C2H4, C2H6, and C3H8. In air separation, permeate purging with a small fraction of the residue stream provides a very effective method for improving module efficiency for drying but is not efficient for improving nitrogen purity or recovery. In multicomponent mixtures, maxima in the compositions of components of intermediate permeability may be observed as a function of distance along the hollow fiber. This result suggests the use of membrane staging to capture these components at their maximum concentration.
TL;DR: In this paper, a general expression for the shear yield stress of a flocculated suspension of particles was derived for the effect of particle size distribution, solid loading, pH, and electrokinetics of the suspension.
Abstract: A general expression was derived for the shear yield stress of a flocculated suspension of particles that is able to describe the effect of particle-size distribution, solid loading, pH, and hence, electrokinetics of the suspension. The model builds on an earlier model by incorporating the effect of the repulsive interaction between particles. Scaling of the data to the maximum yield stress at a given volume fraction provides a means of removing particle-size- and volume-fraction-related effects. The scaling process establishes that to a high level of precision, concentrated dispersions act, in interparticle interaction terms, as the sum of two-body interactions.
TL;DR: In this article, the SAFT model is used in the framework of McMillan-Mayer theory, which considers hard-sphere repulsive, association and dispersion-force interactions.
Abstract: Asphaltene precipitation is a perennial problem in producing and refining crude oils. To avoid precipitation, it is useful to know the solubility of asphaltenes in petroleum liquids as a function of temperature, pressure and liquid-phase composition. In the novel molecular-thermodynamic framework presented here, both asphaltenes and resins are represented by pseudo-pure components while all other components in the solution are represented by a continuous medium that affects interactions among asphaltene and resin particles. The effect of the medium on asphaltene-asphaltene, resin-asphaltene, resin-resin pair interactions is taken into account through its density and dispersion-force properties. To obtain expressions for the chemical potential of asphaltene and for the osmotic pressure of an asphaltene-containing solution, the SAFT model is used in the framework of McMillan-Mayer theory, which considers hard-sphere repulsive, association and dispersion-force interactions. By assuming that asphaltene precipitation is a liquid-liquid equilibrium process, a variety of experimental observations can be explained, including effects of temperature, pressure, and composition on the phase behavior of asphaltene-containing fluids. For practical quantitative applications, the model outlined here requires molecular parameters that must be estimated from a few experimental data.
TL;DR: In this paper, the authors compared the simulated moving bed model (SMB) and the true moving bed approach (TMB) in terms of steady-state performance, internal concentration profiles, and transient behavior of the extract and raffinate purities.
Abstract: Modeling strategies for simulated moving bed adsorbers were studied to compare the simulated moving bed model (SMB) that considers the real shift of the injection and collection points to the true moving bed approach (TMB) that considers liquid and solid flow in opposite directions. The prediction of these two models is compared in terms of steady-state performance, steady-state internal concentration profiles, and transient behavior of the extract and raffinate purities. The influence of the degree of subdivision of the bed in the SMB model predictions is also analyzed and compared with the TMB performance. Model results are compared with experimental results obtained for the chromatographic separation of binaphthol enantiomers.
TL;DR: In this paper, the rectification body method (RBM) is proposed for calculating the minimum energy demand of homogeneous, azeotropic multicomponent distillation processes, which employs all pinch point branches of both column sections and thus requires no a priori selection of active pinch points.
Abstract: Shortcut methods are a prerequisite for the fast evaluation of alternatives in process design. The rectification body method (RBM) for calculating the minimum energy demand of homogeneous, azeotropic multicomponent distillation processes is presented. The new method incorporates both the classical Underwood technique and certain previously proposed techniques as special cases. It employs all pinch point branches of both column sections and thus requires no a priori selection of active pinch points. It is entirely general and can be applied to any type of split of nonideal and azeotropic mixtures irrespective of the number of components. Hence, it significantly extends previous results and practical applicability. Its features are highlighted through examples of nonideal separations with three, four, and five components.
TL;DR: A comprehensive review of the literature on phase transfer catalysis can be found in this paper, which combines the existing knowledge from chemistry with insights into mechanistic and kinetic analysis and mathematical modeling of soluble and insoluble PTC.
Abstract: Phase transfer catalysis (PTC) uses catalytic amounts of phase transfer agents which facilitate interphase transfer of species, making reactions between reagents in two immiscible phases possible. PTC is used widely in the synthesis of various organic chemicals in both liquid-liquid and solid-liquid systems. Existing literature on PTC is chemistry-intensive and a mere handful of recent articles constitute the entire information on engineering analysis. This article reviews the field comprehensively by combining the existing knowledge from chemistry with insights into mechanistic and kinetic analysis and mathematical modeling of soluble and insoluble PTC. By its very nature, PTC involves a series of equilibrium and mass-transfer steps, beside the two main reactions. Neglect of mass-transfer effects can grossly overpredict the conversion of a PTC mediated reaction. A practical way of using PTC, which enables easy separation, is to immobilize the catalyst on a solid support. Mass-transfer limitations and higher costs, however, have precluded its commercial use so far, requiring further analysis of mass-transfer limitations in these complex three-phase systems. The use of PTC, combined with other rate enhancement techniques like sonochemistry, microwaves, electroorganic synthesis, and photochemistry, is being increasingly explored. Applications in this area in the manufacture of organic intermediates and fine chemicals seem almost unlimited.
TL;DR: In this paper, the authors verified the theory of granular flow for flow of fluid catalytic cracking particles in a vertical pipe using a differential transducer and a digital camera as a function of bulk density, determined using an X-ray densitometer.
Abstract: Kinetic theory of granular flow was verified experimentally for flow of fluid catalytic cracking particles in a vertical pipe. Measurements of particle pressure using a differential transducer and granular temperature with a digital camera as a function of bulk density, determined using an X-ray densitometer, showed that a relation exists among pressure, temperature, and density, analogous to the ideal gas law. In the limit of zero solids volume fraction: (Solid Pressure)/[(Granular Temperature) × (Bulk Density)] = 1.0. Measurements of radial distribution functions using the digital camera showed that their peak values occur at particle contact and lie between the predictions from the Bagnold equation and Carnahan–Starling equation. The hard sphere model was corrected for a cohesive pressure using the minimum in the measured radial distribution function. The new model agrees with the pressure measurements in the dense regime.
TL;DR: In this article, a systematic computer-assisted study illustrating the use of two model reduction methodologies (Approximate Inertial Manifolds and the Karhunen-Loeve expansion) in controlling (stabilizing) a nonlinear reaction-diffusion problem is presented.
Abstract: Model reduction methodologies for the partial differential equations modeling distributed parameter systems constitute an important first step in controller design. A systematic computer-assisted study illustrating the use of two such methodologies (Approximate Inertial Manifolds and the Karhunen-Loeve expansion) in controlling (stabilizing) a nonlinear reaction-diffusion problem is presented. The approximation quality of the models, issues of computational implementation of the reduction procedure, as well as issues of closed-loop stability are addressed.
TL;DR: In this article, the structure of the flow in a vessel stirred by a Rushton turbine was investigated using laser Doppler anemometry measurement techniques and the time and length scales of turbulence were determined and used to estimate the dissipation rate of turbulence energy.
Abstract: The structure of the flow in a vessel stirred by a Rushton turbine was investigated using laser Doppler anemometry measurement techniques. The time and length scales of turbulence were determined and used to estimate the dissipation rate of turbulence energy. The levels of turbulence energy and dissipation are high near the turbine and decrease rapidly with increasing distance from the turbine blades. The turbulence in the impeller stream is mostly anisotropic close to the blades. The results are compared with the findings of earlier investigations, and their implications for computational fluid dynamics (CFD) predictions of the flows are discussed.
TL;DR: The differential-algebraic equation (DAE) optimization problem is transformed to a nonlinear programming problem by applying collocation on finite elements using a reduced space successive quadratic programming (rSQP) algorithm, which solves more than 150 DAEs in less than 7 CPU minutes.
Abstract: The differential-algebraic equation (DAE) optimization problem is transformed to a nonlinear programming problem by applying collocation on finite elements. The resulting problem is solved using a reduced space successive quadratic programming (rSQP) algorithm. Here, the variable space is partitioned into range and null spaces. Partitioning by choosing a pivot sequence for an LU factorization with partial pivoting allows us to detect unstable modes in the DAE system, which can now be stabilized without imposing new boundary conditions. As a result, the range space is decomposed in a single step by exploiting the overall sparsity of the collocation matrix; which performs better than the two-step condensation method used in standard collocation solvers. To deal with ill-conditioned constraints, we also extend the rSQP algorithm to include dogleg steps for the range space step that solves the collocation equations. The performance of this algorithm was tested on two well known unstable problems and on three chemical engineering examples including two reactive distillation columns and a plug-flow reactor with free radicals. One of these is u batch column where an equilibrium reaction takes place. The second reactive distillation problem is the startup of a continuous column with competitive reactions. These optimization problems, which include more than 150 DAEs, ure solved in less than 7 CPU minutes on workstation class computers.
TL;DR: In this article, a finite-element algorithm is developed to solve the population balance equation that governs steady-state behavior of well-mixed particulate systems, and the Galerkin method is used to solve several test problems in which aggregation, breakage, nucleation and growth (and combinations of these phenomena) occur.
Abstract: A finite-element algorithm is developed to solve the population balance equation that governs steady-state behavior of well-mixed particulate systems. Collocation and Galerkin methods are used to solve several test problems in which aggregation, breakage, nucleation and growth (and combinations of these phenomena) occur. It is shown that the Galerkin method must be used in growth problems to obtain a well-conditioned system. In all the cases investigated, density distributions and their moments are accurately predicted by the method. In a direct comparison with the discretized population balance (DPB) of Litster et al. (1995) the finite-element method proves capable of predictions that are typically two orders of magnitude more accurate than those of the DPB. These results were obtained using smaller systems of equations and with considerably less computational power.
TL;DR: In this article, the effects of pressure and temperature on the rates of bubble formation, coalescence and breakup, and the initial bubble size and maximum stable bubble size are illustrated, through direct-flow visualization.
Abstract: Hydrodynamic characteristics of bubble columns are studied by considering both the local/bubble-scale and global/column-scale properties of the system, with specific emphasis on their dependency on operating pressure and temperature. The local-scale properties include single-bubble characteristics and interactive dynamics involving bubble coalescence and breakup, while the global-scale properties include gas holdup. Experiments are conducted in a bubble column with a multiorifice ring sparger for pressures as high as 20 MPa and temperatures ranging from 27 to 78°C. Density, viscosity, and surface tension, the liquid phase properties, are measured in situ by using hydrostatic weighing, falling-ball and emerging-bubble techniques, respectively. The bubble behavior is examined through direct-flow visualization. Pressure and temperature affect the bubble rise velocity mainly by varying physical properties of the fluids. Effects of pressure and temperature on the rates of bubble formation, coalescence and breakup, and the initial bubble size and maximum stable bubble size are illustrated. Elevating pressure and/or temperature increases gas holdup; the increasing rate depends on the operating conditions through their effects on the fluid physical properties.
TL;DR: In this article, the adsorption dynamics of a layered bed packed with activated carbon and zeolite 5A were studied experimentally and theoretically through breakthrough experiments and two-bed pressure swing adsorment (PSA) processes by using coke oven gas.
Abstract: The adsorption dynamics of a layered bed packed with activated carbon and zeolite 5A were studied experimentally and theoretically through breakthrough experiments and two-bed pressure swing adsorption (PSA) processes by using coke oven gas (56.4 vol.% H{sub 2}; 26.6 vol.% CH{sub 4}; 8.4 vol.% CO; 5.5 vol.% N{sub 2}; and 3.1 vol.% CO{sub 2}). The results of breakthrough curves of a layered bed showed an intermediate behavior of those of zeolite-5A bed and activated carbon bed, because each concentration front propagates with its own wavefront velocity in each layer by a different adsorption equilibrium. Since a fast and dispersed mass-transfer zone of CO in the zeolite layer of a layered bed leads to a long leading front of the N{sub 2} wavefront, controlling the leading wavefront of the N{sub 2} plays a very important role in obtaining a high-purity product and in determining the optimum carbon ratio of a PSA process for H{sub 2} recovery from coke oven gas. The layered bed PSA process was simulated in a simplified form of two single-adsorbent beds linked in series. The dynamic model incorporating mass, energy, and momentum balances agreed well with the experimental data. Concentration profiles inside the adsorption bed were alsomore » investigated.« less
TL;DR: In this article, a methodology is developed for finding a window of operating conditions within which one should be able to produce a product having a specified set of quality characteristics, using historical data on the process obtained during the production of a range of existing product grades.
Abstract: A methodology is developed for finding a window of operating conditions within which one should be able to produce a product having a specified set of quality characteristics. The only information assumed to be available is that contained within historical data on the process obtained during the production of a range of existing product grades. Multivariate statistical methods are used to build and to invert either linear or nonlinear empirical latent variable models of the existing plant operations to obtain a window of operating conditions that are capable of yielding the desired product and that are still consistent with past operating procedures and constraints. The methods and concepts are illustrated using a simulated high-pressure tubular reactor process for producing low-density polyethylene.