Showing papers in "Aiche Journal in 1991"

Nonlinear principal component analysis using autoassociative neural networks

Abstract: Nonlinear principal component analysis is a novel technique for multivariate data analysis, similar to the well-known method of principal component analysis. NLPCA, like PCA, is used to identify and remove correlations among problem variables as an aid to dimensionality reduction, visualization, and exploratory data analysis. While PCA identifies only linear correlations between variables, NLPCA uncovers both linear and nonlinear correlations, without restriction on the character of the nonlinearities present in the data. NLPCA operates by training a feedforward neural network to perform the identity mapping, where the network inputs are reproduced at the output layer. The network contains an internal “bottleneck” layer (containing fewer nodes than input or output layers), which forces the network to develop a compact representation of the input data, and two additional hidden layers. The NLPCA method is demonstrated using time-dependent, simulated batch reaction data. Results show that NLPCA successfully reduces dimensionality and produces a feature space map resembling the actual distribution of the underlying system parameters.

Mathematical model of a gas diffusion electrode bonded to a polymer electrolyte

Abstract: A mathematical model for an ion-exchange membrane attached to a gas-fed porous electrode is derived and discussed. The model is applied to simulate the oxygen electrode of a polymer-electrolyte fuel cell. Our discussion focuses on cell polarization characteristics, water transport, and catalyst utilization—all of which must be considered for fuel-cell design. Calculated polarization behavior is shown to compare favorably with published experimental data. Our results indicate that if the membrane maintains full saturation, its contribution to the total cell resistance is most significant at higher operating current densities (greater than 200 mA/cm2). Polarization resistance due to the oxygen reduction reaction appears to be important for all practical current densities. Water transport, driven by pressure and electric-potential forces, is shown to be a complicated function of the cell operating conditions. The utilization and distribution of noble-metal catalyst is discussed.

Curvature and parametric sensitivity in models for adsorption in micropores

Abstract: The sensitivity of the calculated micropore size of zeolite Y in a fluidized cracking catalyst based on empirical models for argon adsorption has been tested by examining the effect of curvature and by systematically verifying the magnitude of physical constants in the model equations. With a consistent set of physical parameters the slit model provided a pore size value of 0.45 nm, while the new cylindrical models provided values of 0.69 and 0.74 nm. The latter values are found to correspond well with the known aperture size of zeolite Y, 0.74 nm. By separately varying the magnitudes of five of the physical constants in the model over a range of ±30%, it was concluded that the diameter of the oxide ion at the surface had a large effect on the calculated pore size, while the other parameters had only moderate to small effects. Preliminary application of the cylindrical pore model to isotherms of argon on other zeolites and molecular sieves leads to promising results, especially for medium to large pore zeolites. These results suggest that the cylindrical pore model is a useful means for the transformation of argon adsorption data on a zeolite into a micropore size distribution.

Use of Hammerstein Models in Identification of Nonlinear Systems

Abstract: The utility of the Hammerstein model, which is composed of a static nonlinear element in series with a linear dynamic part, was investigated to represent the dynamics of nonlinear chemical processes. Different methods to identify the parameters of Hammerstein models were tested. The methods were applied to the identification of simulated distillation columns and to an experimental heat exchanger process. The results show that the dynamics of such processes can be better represented by Hammerstein-type models than by linear models.

Generalized kinetic model for wet oxidation of organic compounds

Abstract: A generalized kinetic model for wet oxidation (WO) of organic compounds was developed based on a simplified reaction scheme considering acetic acid as the rate-limiting intermediate. The selectivity of product vs. intermediate formations was quantified by the ratio of the two reaction rate constants. This point selectivity α may be used to characterize the “strength” of the feed stream to be treated. This global model was validated using WO kinetic data reported for temperatures ranging from 150°C to 550°C and pressures varying from 20 bar to 440 bar. Organic conversions predicted by this model, as compared to other models, more accurately reflect the actual performance of WO processes. The model has practical validity for a variety of organic compounds, wastewaters and sludges in both subcritical and supercritical water oxidation processes.

A molecular mechanism for gas hydrate nucleation from ice

Abstract: Induction phenomena are explained that exist in the only two reproducible sets of kinetic data in the literature for gas hydrate formation from an agitated ice surface. The previously unexplained data are interpreted using recent crystal diffraction results. The induction explanation is validated through cyclopropane hydrate kinetic experiments. The induction reasoning forms the basis of an hypothesis for a molecular mechanism of hydrate formation from ice. The hypothesized mechanism is quantified and given physical interpretation. The hypothesis may have significant implications for inhibiting hydrate formation.

Diffusive and convective protein transport through asymmetric membranes

Abstract: The objective of this study was to obtain quantitative data on combined convective and diffusive transport of bovine serumalbumin (BSA) through the highly constricted pores of asymetric ultrafiltration membranes with a range of nominal molecular weight cutoffs.

A group contribution approach to computer‐aided molecular design

Abstract: A flexible and structured methodology for the computer-aided molecular design (CAMD) by the group contribution approach is presented. The proposed CAMD algorithm takes the following four steps: 1. preselect groups and target properties; 2. generate only a feasible set of compound structures in an optimal fashion; 3. predict properties for the screening of the set of feasible compound structures; and finally 4. select/design the compound. Since the success of any CAMD algorithm depends to a large extent on its ability to predict/compute the needed properties, the importance of the choice and applicability of these methods is considered along with the computational aspects related to the development of a computer program based on the proposed methodology. Finally, the scope of CAMD technology is highlighted using several practical examples.

On‐line inference of polymer properties in an industrial polyethylene reactor

Abstract: A major difficulty affecting the control of product quality in industrial polymerization reactors is the lack of suitable on-line polymer property measurements. In this article a scheme is developed to predict melt index and density in a fluidized-bed ethylene copolymerization reactor. Theoretically-based models are derived to predict quality variables from the available on-line temperature and gas composition measurements. Adjustable parameters in these models are updated on-line using infrequent laboratory measurements and a recursive parameter estimation technique. The application of this methodology is illustrated using operating data from an industrial reactor. It is shown that both melt index and density can be successfully predicted. Knowledge of product property deviations from desired targets is required so that manufacturers can take corrective actions to reduce the quantity of off-grade material made and produce a consistent product.

Mathematical model of the hydrocyclone based on physics of fluid flow

Abstract: A mathematical model of the hydrocyclone, based on the physics of fluid flow, has been developed. The model equations are solved in a computer code that takes as input the hydrocyclone dimensions and feed slurry characteristics. The output of the computer code is the velocity profiles of the fluid and the separation efficiency curve. To validate the model, an LDV was used to measure the velocity profiles inside a 75-mm hydrocyclone. Pure water and glycerol-water mixture were used as the working media to simulate the increase of slurry viscosity in the presence of solid particles. The predicted velocity profiles agree well with the experimental measurements. Dilute limestone slurry was also classified with the same hydrocyclone, and predicted the separation efficiency curve shows good agreement with experimental observation.

Growth and transformation of TiO2 crystallites in aerosol reactor

Abstract: Rate process concerning the formation of TiO2 fine crystalline particles by the gas-phase reaction of TiCl4 and O2 are studied using aerosol reactors. Chemical reaction of TiCl4, sintering of particles, mixing of reactants, and transformation from anatase to rutile are evaluated as the system parameters of the simulation model proposed. The crystallite size in the range of 55–65 nm at 1,273 K is predicted well by a model that assumes the maximum fusible particle size, 15 nm in this case. The defect concentration in the TiO2 crystallites strongly affects the transformation rate, and anatase particles produced at 1,173 K are transformed to rutile more rapidly than those produced at 1,373 K. The transformation is simulated quantitatively by the model with the coordinates for elapsed time, particle size and rutile fraction. The model can be applied to such particle production processes as collision, sintering and crystal transformation occurring simultaneously.

Fault diagnosis in complex chemical plants using artificial neural networks

Abstract: We illustrate a neural network approach to fault detection and diagnosis in a large complex chemical plant. We demonstrate the ability of a neural network to learn nonlinear mappings in the presence of noisy inputs. We also show that neural network models can exhibit the rule-following behavior of knowledge-based expert systems without containing any explicit representations of the rules. We conclude that, given a valid database, fault detection and diagnosis is a promising area for the application of artificial neural networks in industry

An internal model control strategy for nonlinear systems

Abstract: An internal model control (IMC) strategy for nonlinear single-input single-output systems is proposed. The controller is designed to provide nominal performance, and a nonlinear filter is added to make the controller implementable and to account for plant/model mismatch. An important advantage of the new approach is that the assumption of full-state feedback inherent in most input-output linearization schemes is eliminated. However, the proposed IMC strategy is restricted to open-loop stable systems with stable inverses. Under mild assumptions, the closed-loop system possesses the same stability, perfect control, and zero offset properties as linear IMC. Simulation results for a continuous fermentor illustrate the advantages of the nonlinear IMC strategy.

Analysis of microwave heating of materials with temperature-dependent properties

Abstract: In this paper transient temperature profiles in multilayer slabs are predicted, by simultaneously solving Maxwell's equations with the heat conduction equation, using Galerkin-finite elements. It is assumed that the medium is homogeneous and has temperature-dependent dielectric and thermal properties. The method is illustrated with applications involving the heating of food and polymers with microwaves. The temperature dependence of dielectric properties affects the heating appreciably, as is shown by comparison with a constant property model.

Prediction of the three-dimensional turbulent flow in stirred tanks

Abstract: Efforts to model the turbulent flow in stirred tanks require accurate boundary conditions at the tip of the impeller, not just of velocities, but of the turbulence quantities k and e. Kolar's (1982) phenomenological, swirling radial jet model of the impeller region is extended by using a two-equation k – e turbulence model to obtain direct estimates of k and e on the impeller periphery. The model is extended and clarified, so that the number of parameters required for its application is reduced to two: the rotational speed and the diameter of the impeller. Three-dimensional simulations allow a realistic treatment of the baffles. Agreement of the modeling results with recently published experimental data is excellent. This is particularly true in the important impeller discharge zone, where details of the predicted behavior of the turbulence kinetic energy and dissipation rate are in quantitative agreement with the available data. Based on these results, average values of e are calculated, along with the zones over which the apply. For the impeller discharge zone, the dimensionless, volume-averaged e is 0.19.

Vapor synthesis of titania powder by titanium tetrachloride oxidation

Abstract: Formation of titania particles by vapor-phase oxidation of titanium tetrachloride was studied in an aerosol reactor between 1,200 and 1,723 K. The effect of process variables (reactor residence time, temperature, and reactant concentration) on powder size and phase characteristic was investigated using the differential mobility particle sizer, scanning electron microscopy, and X-ray diffraction. Titania particles were primarily anatase though the rutile weight fraction increased with increasing reactor temperature. The geometric number average diameter of the particles was between 0.13 and 0.35 μm, and the geometric standard deviation of the particle size distribution was about 1.4. The average particle size increased with increasing temperature, inlet TiCl4 concentration, and residence time. The observed changes in the particle size distribution were compared with those predicted by solving the aerosol dynamic equation by a sectional method and accounting for coagulation and first-order chemical reaction. While variations in the process variables resulted in discernible changes in the size of the particles, the spread of the distribution remained rather unaffected.

Chemical, quasi‐chemical and perturbation theories for associating fluids

Abstract: Pure fluids and mixtures of species that hydrogen bond behave differently from systems that interact only through dispersion forces. The deviations from classical behavior often are sufficiently large that conventional equations of state and activity models cannot be used without the introduction of large, condition-dependent empirical parameters. Consequently, three different classes of theories have been developed specifically to treat hydrogen-bonding systems. The first is based on the assumption that when molecules hydrogen-bond, they react to form new species and consequently is referred to as “chemical” theory. The second is based on lattice-fluid theory that is used to describe different types of specific interactions and is known as “quasi-chemical” theory. The last is based on the solution of integral equations using a potential function that mimics that of a hydrogen bond. It is shown here that these three approaches give essentially equivalent results. This allows one to relate the parameters in the perturbation theory to the equilibrium constant and hence greatly improves its utility for real systems. All three theories are compared with simulation data.

Prediction of gas adsorption in 5a zeolites using monte carlo simulation

Abstract: Adsorption of air in 5A zeolites was studied using Monte Carlo simulations in the grand canonical ensemble (μ, V, T constant). Site-site potentials were used to model the adsorbate-zeolite and adsorbate-adsorbate interactions. The potential model contains one adjustable parameter that was fit to a single experimental isotherm data point. Adsorption isotherms and heats of adsorption were determined for pure argon, oxygen, and nitrogen at 203.15 K, 233.15 K, and 297.15 K from 0.1 bar to 4.0 bar. Multicomponent adsorption isotherms were determined for binary mixtures of oxygen and nitrogen at 203.15 K. The results for the pure-component isotherms are in excellent agreement with experimental data. The results for the heat of adsorption are in good agreement with experimental data for argon and oxygen, but not for nitrogen. The results for multicomponent adsorption isotherms are qualitatively correct; however, the simulation was not able to quantitatively predict mixture data.

Flow characteristics of waxy crude oils: Application to pipeline design

Abstract: Waxy crude oils are highly non-Newtonian materials known to cause handling and pipelining difficulties and whose flow properties are time- and history-dependent. In this paper experimental techniques are described that enable reproducible steady-state flow property data to be obtained from rotational viscometers. The flow properties are shown to depend strongly on the shear rate applied during cooling (shear history effect). This leads to a definable minimum operating point below which flow in a waxy crude oil pipeline would cease. Modified pipeline design techniques are presented for both laminar and turbulent flow at temperatures below the pour point, and it is shown that existing techniques overestimate the flow rate in laminar flow by the order of 100%. The modified design techniques can be used to quantitatively assess the performance of flow improver (pour point depressant) additives under steady-state conditions.

Gas‐solid flow in vertical tubes

Abstract: This paper reports on a computational study of fully-developed flow of gas-particle suspensions in vertical pipes which was carried out, using the model proposed recently by Sinclair and Jackson, to understand the predicted scale-up characteristics. It was shown that the model can capture the existence of steady-state multiplicity wherein different pressure gradients can be obtained for the same gas and solids fluxes. A pronounced and nonmonotonic variation of the pressure gradient required to achieve desired fluxes of solid and gas with tube diameter was predicted by the model, and this is explained on a physical basis. The computed results were compared with the experimental data. The model manifests an unsatisfactory degree of sensitivity to the inelasticity of the particle-particle collisions and the damping of particle-phase fluctuating motion by the gas.

A generalized Blake‐Kozeny equation for multisized spherical particles

Abstract: The objectives of this study were twofold First, in view of the pausicity of data in the literature, additional experiments were conducted for laminar flow through a porous medium made up of multisized particles Second, a theoretical analysis was performed to provide a physical basis for correlating the permeability data

Airlift bioreactors: Analysis of local two‐phase hydrodynamics

Abstract: Local two-phase flow measurements were obtained in a pilot-scale, external-loop airlift bioreactor using hot-film anemometry and resistivity probe techniques. The radial dependence of both gas and liquid velocities and of the void fraction was substantial. Developing flow effects were pronounced, as evidenced by distinct changes in the radial profiles of fluid flow properties with axial position. For high gas flow rates, liquid acceleration effects near the sparger resulted in greatly reduced slip velocities in a substantial portion of the riser. A significant reduction in mass transfer may occur under such conditions. The point equations of continuity and motion were used to develop a differential, two-fluid model for two-phase flow in airlift risers. The only empirical parameters in the model represent frictional effects. The developing two-phase flow characteristic of airlift risers was observed to create significantly higher frictional effects at the wall than is routinely observed for fully-developed flow. Model predictions were compared to our own experimental results as well as those of Merchuk and Stein (1981). Agreement between the predicted and measured values was typically within 10% for both cases.

Multiple steady states in ideal two‐product distillation

Abstract: Simple distillation columns with ideal vapor-liquid equilibrium may display multiple steady-state solutions. Two fundamentally different sources for the multiplicity are presented. Both bring about the unexpected result that increasing reflux makes separation worse in the top part of the column. It corresponds to an unstable operating point. The first type of multiplicity is found for columns with mass or volume inputs (e.g., mass reflux and molar boilup). Even for constant molar flows, the transformation from the actual input units to molar units may become singular (corresponding to a pitchfork bifurcation point), resulting in multiple steady-state solutions. The results are highly relevant in practice, as industrial columns usually have inputs on a mass or volume basis. The second type for specifications on a molar basis (e.g., molar reflux and molar boilup) depends on the presence of an energy balance in the model. The multiplicity is caused by interactions between flows and compositions in the column.

Effective Kundsen diffusivities in structures of randomly overlapping fibers

Abstract: Effective Knudsen diffusion coefficients are presented for fibrous structures consisting of overlapping fibers. The fibers are distributed randomly in d (d=2 or 3) directions with their axes perpendicular to one direction (d=2) or in the three-dimensional space with no preferred orientation (d=3), or they are grouped into d (d=1, 2, or 3) mutually perpendicular bundles of parallel, randomly overlapping fibers. Effective diffusivities are computed using a Monte Carlo simulation scheme to determine the mean square displacement of molecules traveling in the interior of the porous medium for large travel times. Our results show that structures with fibers distributed randomly in d directions have diffusion coefficients identical, within the accuracy of our simulation, to those of d-directional, parallel fiber structures. Effective Knudsen diffusivities are strongly influenced only by the directionality of the fiber structure, with tridirectional or randomly oriented fiber structures presenting lower percolation thresholds (0.04 vs. 0.11) and higher effective diffusivities than bidirectional or random structures with their axes perpendicular to one direction. The tortuosity factor is in general found to decrease with increasing porosity, approaching for each case, as the porosity goes to unity, the corresponding lower bound that is derived using variational principles.

Molecular thermodynamics of solubilities in gas antisolvent crystallization

Abstract: An expanded liquid molecular thermodynamic model is developed to predict the solubilities of pure solids in a liquid expanded with a gaseous antisolvent. Experimental data are presented for systems containing naphthalene, phenanthrene, and a mixture of both in toluene expanded with a gas antisolvent, CO2. The pressure range is 1 to 64 bar and the temperature is 25°C. The data are predicted accurately with regular solution theory up to moderate pressures, but not at the higher pressures where the liquid phase is nearly pure CO2. In contrast, the new expanded liquid equation of state model describes the wide range of behavior from the nearly ideal liquid solution at ambient pressure to the highly nonideal compressible fluid at elevated pressures. As a result, it predicts solubilities accurately over three orders of magnitude by using only binary interaction parameters. The implications of the phase behavior on fractional crystallization with a gas antisolvent are discussed.

Quantitative description of ultrafiltration in a rotating filtration device

Abstract: A correlation was developed to quantitatively describe the flux in a high-speed rotating filtration device using a minimum set of parameters. The experimental results were found to be consistent with the concentration polarization (CP) model. Beyond a threshold pressure flux ceases to depend on membrane permeability. The CP model was modified to include the concentration dependence of the diffusivity. This approach was found to be consistent with the strong dependence of flux on pH. Protein concentration in the polarized layer adjacent to the membrane surface was estimated using a procedure that corrects for some of the inconsistencies in the methods usually applied. Four dimensionless numbers were necessary to correlate the experiments with good accuracy. Previously-reported correlations used only three dimensionless numbers. Usage of four numbers could be justified by dimensional analysis. Finally, the performance of rotary or vortex filtration was compared to that of other configurations.

Diffusion in ion-exchanged clinoptilolites

Abstract: The two-dimensional channel structure of clinoptilolite has been altered systematically by ion exchange to study the effects of cation type, size, location, and distribution on the diffusion of N2 and CH4 probe molecules. Concentration-dependent diffusion time constants (D/L2) were determined from gravimetric uptake measurements for fully-exchanged K+, Na+, and H+ clinoptilolites, and highly-exchanged Ca2+ (89%) and Mg2+ (72%) clinoptilolites. Both plane sheet and parallel channel diffusion models were developed from the one-dimensional plane sheet diffusion equation and fit to the uptake data. Resulting values of D/L2 varied by a factor of more than 1,000 for both N2 and CH4, while kinetic selectivity spanned nearly two orders of magnitude for this group of modified clinoptilolites. Achieving this range in performance for the difficult N2/CH4 separation demonstrates the excellent potential for tailoring clinoptilolite by cation manipulation for the kinetic separation of other gas mixtures.

Stability of SISO quadratic dynamic matrix control with hard output constraints

Abstract: The inclusion of output constraints in the on-line optimization problem solved by quadratic dynamic matrix control (QDMC) can result in a unstable, closed-loop system, even when the corresponding unconstrained algorithm is stable. The presence of constraints in the optimization problem produces a nonlinear, closed-loop system, although the plant and model dynamics are assumed linear. This article quantifies the effect of output constraints on both nominal and robust stability for single-input/single-output processes. Stability conditions provided can be used to select the QDMC parameters and constraint window. Examples demonstrate that these conditions can capture the nonlinear effect of the constraints and that tuning rules developed for the unconstrained case should not be used with output constraints. An example with dead time error illustrates the use of this framework to guarantee the robustness of constrained QDMC with respect to modeling error.

Pillared clays as a new class of sorbents for gas separation

Abstract: High-surface-area, Zr-pillared, layered clays are synthesized and characterized for their adsorption properties Although large free interlayer spacings are claimed in the literature (as also found in this work, 143 A), the limiting pore size is the narrow interpillar spacing The distribution of interpillar spacing is determined by molecular probing and adsorption data along with a theoretical framework available from the literature Interpillar spacing can be tailored by controlling the number density of pillars inserted during the ion exchange (oligomer inserting) step The following variables in the ion exchange solution result in lowering the pillar density: higher pH, lower oligomer concentration, and introduction of competitive cations By changing these variables, peak interpillar spacing is shifted by nearly 2 A (from 5 to 7 A) The versatility of pillared clays as sorbents for kinetic separation (ie, separation based on diffusivity differences) has been demonstrated by the separations of air and xylene isomers