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Showing papers in "Aiche Journal in 1993"


Journal ArticleDOI
TL;DR: In this article, the linear model predictive control concepts were discussed in a unified theoretical framework based on a stabilizing, infinite horizon, linear quadratic regulator for the plant model.
Abstract: This article discusses the existing linear model predictive control concepts in a unified theoretical framework based on a stabilizing, infinite horizon, linear quadratic regulator. In order to represent unstable as well as stable multivariable systems, the standard state-space formulation is used for the plant model. The incorporation of a nominally stabilizing constrained regulator eliminates the current requirement of tuning for nominal stability. Output feedback is addressed in the well-established framework of the linear quadratic state-estimation problem. This framework allows the flexibility to handle nonsquare systems, noisy inputs and outputs, and nonzero input, output, and state disturbances. This formulation subsumes the integral control schemes designed to remove steady-state offset currently in industrial use. The online implementation of the controller requires the solution of a standard quadratic program that is no more computationally intensive than existing algorithms.

706 citations


Journal ArticleDOI
TL;DR: In this article, the role of thin films in porous media is explored and a collection of star-shaped capillary tubes model is proposed to describe the geological development of mixed-wettability in reservoir rock.
Abstract: Understanding the role of thin films in porous media is vital if wettability is to be elucidated at the pore level. The type and thickness of films coating pore walls determines reservoir wettability and whether or not reservoir rock can be altered from its initial state of wettability. Pore shape, especially pore wall curvature, is an important factor in determining wetting-film thicknesses. Yet, pore shape and the physics of thin wetting films are generally neglected in models of flow in porous rocks. This paper incorporates thin-film forces into a collection of star-shaped capillary tubes model to describe the geological development of mixed-wettability in reservoir rock. Here, mixed-wettability refers to continuous and distinct oil and water-wetting surfaces coexisting in the porous medium. The proposed model emphasizes the remarkable role of thin films. New pore-level fluid configurations arise that are quite unexpected. For example, efficient water displacement of oil (i.e, low residual oil saturation) characteristic of mixed-wettability porous media is ascribed to interconnected oil lenses or rivulets which bridge the walls adjacent to a pore corner. Predicted residual oil saturations are approximately 35 % less in mixed-wet rock compared to completely water-wet rock. Calculated capillary pressure curves mimic those of mixed-wet porousmore » media in the primary drainage of water, imbibition of water, and secondary drainage modes. Amott-Harvey indices range from {minus}0.18 to 0.36 also in good agreement with experimental values. (Morrow et al, 1986; Judhunandan and Morrow, 1991).« less

415 citations


Journal ArticleDOI
TL;DR: In this article, the optimal and robust design of a four-section countercurrent adsorption separation unit is investigated in the frame of equilibrium theory, using a model where the ad-ption equilibria are described through the constant selectivity stoichiometric model, while mass transfer resistances and axial mixing are neglected.
Abstract: The separation of a binary mixture, using a third component having intermediate adsorptivity as desorbent, in a four section countercurrent adsorption separation unit is considered. A procedure for the optimal and robust design of the unit is developed in the frame of Equilibrium Theory, using a model where the adsorption equilibria are described through the constant selectivity stoichiometric model, while mass-transfer resistances and axial mixing are neglected. By requiring that the unit achieves complete separation, it is possible to identify a set of implicity constraints on the operating parameters, that is, the flow rate ratios in the four sections of the unit. From these constraints explicit bounds on the operating parameters are obtained, thus yielding a region in the operating parameters space, which can be drawn a priori in terms of the adsorption equilibrium constants and the feed composition. This result provides a very convenient tool to determine both optimal and robust operating conditions. The latter issue is addressed by first analyzing the various possible sources of disturbances, as well as their effect on the separation performance. Next, the criteria for the robust design of the unit are discussed. Finally, these theoretical findings are compared with a set of experimentalmore » results obtained in a six port simulated moving bed adsorption separation unit operated in the vapor phase.« less

370 citations


Journal ArticleDOI
TL;DR: In this article, a 19-elementary-step model of adsorption, desorption and surface reaction steps with reaction parameters from the literature or from fits to previous experiments was used to simulate the direct oxidation of CH4 to H2 and CO in O2 and in air at high temperatures over alumina foam monoliths.
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 CH4rich conditions at high temperatures, H2 and CO are primary products of the direct oxidation of methane via a pyrolysis mechanism.

350 citations


Journal ArticleDOI
TL;DR: In this article, a 1 wt. % polystyrene in toluene solution into CO2 through a 100-μm nozzle is formed with diameters from 0.1 to 20 μm.
Abstract: Polymer microspheres and fibers are formed with a versatile new process, precipitation with a compressed fluid antisolvent. By spraying a 1 wt. % polystyrene in toluene solution into CO2 through a 100-μm nozzle, microspheres are formed with diameters from 0.1 to 20 μm as the CO2 density decreases from 0.86 to 0.13 g/cm3. The uniform submicron spheres produced at high CO2 density are due in part to the rapid atomization produced by the large intertial and low interfacial forces. Fibers, with and without microporosity, are obtained at higher polymer concentrations where viscous forces stabilize the jet. The effect of CO2 density and temperature on the size, morphology and porosity of the resulting polymeric materials is explained in terms of the phase behavior, spray characteristics, and the depression in the glass transition temperature.

312 citations


Journal ArticleDOI
TL;DR: In this article, the authors calculate permeabilities for a class of granular porous media derived from a real, disordered packing of equal spheres, where the entire structure including pore space of these media is completely specified by the radii and spatial locations of the constituent grains.
Abstract: The authors calculate permeabilities for a class of granular porous media derived from a real, disordered packing of equal spheres. The entire structure, including pore space, of these media is completely specified by the radii and spatial locations of the constituent grains. When geometric nearest neighbor grains are grouped together, the structure may be subdivided into pore bodies and pore throats in a natural and unambiguous way. From this subdivision one can establish a network of flow paths whose geometry and topology are completely specified, so that permeability and other transport coefficients can be calculated directly and without any adjustable parameters. The calculations focus on processes that form porous media, rather than on specific examples of such media. Hence, the approach is essentially predictive, rather than correlative. No additional measurements (such as capillary pressure data or pore system data from thin sections) are required, and correlations between permeability and other properties are not used. Predicted permeabilities match measurements on sandstone sample similar to the model porous media studied here over a wide range of porosity. Geometrical attributes of the network representation of the pore space of the model media are found to be spatially correlated. This departure from randomness significantlymore » affects permeability. The agreement between predictions and measurements suggests that spatial correlation is inherent in granular porous media and that uncorrelated network models are therefore unlikely to be physically representative of such media.« less

261 citations


Journal ArticleDOI
TL;DR: In this paper, a Monte Carlo simulation scheme was employed to determine the effective diffusivities from the mean-square displacement of random walkers traveling in the interior of the porous structure, and it was found that the effect of the orientational distribution of the fibers, porosity of the fibrous structures, and the Knudsen number depend strongly on the diffusivity.
Abstract: The problem of bulk, transition and Knudsen regime diffusion in structures of freely overlapping fibers of various orientation distributions was numerically investigated, and the interrelation of the resulting effective diffusivities was examined. Fibers were randomly positioned and oriented in d = 1, 2, or 3 directions. A Monte Carlo simulation scheme was employed to determine the effective diffusivities from the mean-square displacement of random walkers traveling in the interior of the porous structure. The effective diffusivity was found to depend strongly on the orientational distribution of the fibers, porosity of the fibrous structures, and Knudsen number. The tortuosity factor decreased in general with increasing porosity, approaching at the limit of dilute beds the lower bound derived for each direction of diffusion from variational principles. The simulation results agreed well with experimental values of the bulk tortuosity of fibrous beds from the literature. It was also found that the reciprocal additivity or harmonic average effective diffusivity expression (Bosanquet formula), commonly used to estimate transition regime diffusivities from the values at the ordinary and Knudsen diffusion limits, provides an excellent approximation for the effective diffusivity of fibrous beds, except for that parallel to the fibers of a unidirectional structure.

256 citations


Journal ArticleDOI
TL;DR: This article presents the mathematical framework for the development of Wave-Nets and discusses the various aspects of their practical implementation and presents two examples on the application; the prediction of a chaotic time-series, representing population dynamics, and the classification of experimental data for process fault diagnosis.
Abstract: A Wave-Net is an artificial neural network with one hidden layer of nodes, whose basis functions are drawn from a family of orthonormal wavelets. The good localization characteristics of the basis functions, both in the input and frequency domains, allow hierarchical, multiresolution learning of input-output maps from experimental data. Furthermore, Wave-Nets allow explicit estimation for global and local prediction error-bounds, and thus lend themselves to a rigorous and explicit design of the network. This article presents the mathematical framework for the development of Wave-Nets and discusses the various aspects of their practical implementation. Computational complexity arguments prove that the training and adaptation efficiency of Wave-Nets is at least an order of magnitude better than other networks. In addition, it presents two examples on the application of Wave-Nets; (a) the prediction of a chaotic time-series, representing population dynamics, and (b) the classification of experimental data for process fault diagnosis.

240 citations


Journal ArticleDOI
TL;DR: In this article, a new equation of state for electrolyte solutions has been developed from an expression of the Helmholtz free energy containing a nonelectrolyte part and a part relative to ions.
Abstract: A new equation of state for electrolyte solutions has been developed from an expression of the Helmholtz free energy containing a nonelectrolyte part and a part relative to ions. The nonelectrolyte part is taken from the equations of state (EOS) of Schwartzentruber et al. (1989). The ionic part is composed of an MSA long-range term to account for electrostatic interactions and a short-range interaction term specific to ions. Using correlations between parameters and experimental ionic diameters, the model reduce to a one-parameter model. It has been applied to numerous strong electrolyte systems and extended to ternary systems to test its predictability without mixing parameters for ions. Its results compare well to the results reported for other one-parameter models (electrolyte EOS). Furthermore, it was found that the cation-anion interaction parameter could also be correlated to experimental ionic diameters. Then, the osmotic coefficients of 28 alkaline and alkaline-earth halide systems may be represented with a root mean square relative deviation of 2.9% using only six correlation parameters. This result has been extended to other systems, with the conclusion that the model with all parameters correlated may also be applied to systems other than halide solutions. The resulting model is predictive. The quality of the prediction was tested by determining osmotic coefficients relative to six systems without any parameter adjustment. The deviations of the predicted values range from 2.0 to 5.4%. The quality of the representation of mixed salts systems without mixing parameters was evaluated using experimental osmotic coefficients of 30 ternary systems.

176 citations


Journal ArticleDOI
TL;DR: A generalized least-squares regression analysis is proposed that predicts the precision of the indices based on their assumed true values and provides a means to address such issues as optimal sampling methods for data acquisition from cell tracks and handling errors associated with measuring cell position.
Abstract: Active cell migration is essential in many physiological processes and in the function of some bioartificial tissues. Therefore, several investigators have recently attempted to quantitatively characterize random cell movement on isotropic substrata in vitro. A popular approach is to fit a theoretical expression for mean-squared cell displacement deriving from correlated random walk models to cell tracking data, yielding three objective cell movement indices: root-mean-squared speed, directional persistence time, and random motility coefficient (analogous to a molecular diffusion coefficient). The data are obtained typically by averaging cell displacements over a cell track composed of cell positions measured at equal time increments and frequently by further pooling such displacement data from tracks of different cells from the same population. We identify pitfalls introduced if an ordinary nonlinear least-squares regression analysis is used to fit the theoretical expression to the data as is commonly done and propose a generalized least-squares regression analysis as a remedy. This method estimates the cell movement indices and associated uncertainties much more accurately. It also predicts the precision of the indices based on their assumed true values and provides a means to address such issues as optimal sampling methods for data acquisition from cell tracks and handling errors associated with measuring cell position.

161 citations


Journal ArticleDOI
TL;DR: The equilibrium and dynamics of toluene adsorption and desorption in single component aqueous solutions were investigated in this article, where the dependence of the external mass-transfer coefficient on the hydrodynamic conditions in the liquid phase was taken into account.
Abstract: The equilibrium and dynamics of toluene adsorption and desorption in singlecomponent aqueous solutions were investigated. Adsorption rates in a batch reactor under a variety of operating conditions were fitted successfully with the homogeneous surface diffusion model and a surface diffusion coefficient that increases exponentially with surface concentration. The dependence of the external mass-transfer coefficient on the hydrodynamic conditions in the liquid phase was taken into account. Desorption studies in the aqueous phase and solvent regeneration of tolueneloaded activated carbon suggest that only a small fraction of toluene adsorbs irreversibly. Moreover, irreversible adsorption occurs only on virgin activated carbon, while adsorption on solvent-regenerated activated carbon is fully reversible. After accounting for irreversible adsorption, the model successfully predicted toluene desorption rates in the aqueous phase under various operating conditions using toluene transport parameters determined from the adsorption studies.

Journal ArticleDOI
TL;DR: In this paper, the problem of selecting the variables to be measured in order to maximize process reliability was tackled in previous articles (Ali and Narasimhan, 1993) and extended to the optimal design of sensor networks for bilinear processes.
Abstract: The problem of selecting the variables to be measured in order to maximize process reliability was tackled in our previous articles (Ali and Narasimhan, 1993, 1995) In this article, this approach is extended to the optimal design of sensor networks for bilinear processes Diverse processes, such as a mineral beneficiation plant, a separation system of a synthetic juice plant, and a crude preheat train of a refinery are used to illustrate the utility of this approach

Journal ArticleDOI
TL;DR: In this article, the authors studied the carbon reduction kinetics to synthesize SiC under conditions of high carbon/silica precursor heating rates and minimized reaction times (s) over a wide temperature range (1,848 [le]T[le]2,273 K).
Abstract: Carbothermal reduction kinetics to synthesize SiC is studied under conditions of high carbon/silica precursor heating rates (10[sup 5] K/s) and minimized reaction times (s) over a wide temperature range (1,848 [le]T[le]2,273 K). The reaction mechanism includes rapid formation of a gaseous SiO intermediate. Further carbon reduction of the SiO to SiC is reaction-rate-controlling. Carbon crystallite diameter, d, has a substantial influence on the rate of reaction and the size of synthesized SiC. Fractional oxide conversion, X, can be described by a contracting volume shrinking core model: k = [1 [minus] (1[minus]x)[sup 1/3]]/t = (k[sub o]/d)exp([minus]E/RT). Where k[sub o] = 27.4 m/s and E = 382 [plus minus] 34 kJ/mol.

Journal ArticleDOI
TL;DR: The input-output model used (polynomial ARMA models) is briefly introduced, and its stability and invertibility are analyzed, paving the way to the development of a nonlinear-model-predictive controller.
Abstract: Most of the advanced nonlinear control algorithms require a model of the system to be controlled. Unfortunately, most of the processes in the chemical industry are nonlinear, and fundamental models describing them are lacking. Thus there is a need for the identification and control of nonlinear systems through available inputoutput data. In this article, we briefly introduce the input-output model used (polynomial ARMA models), and analyze its stability and invertibility. This paves the way to the development of a nonlinear-model-predictive controller. Implementation issues such as modeling of disturbance, state and parameter estimation are discussed. The theory presented is illustrated through examples.

Journal ArticleDOI
TL;DR: In this paper, sufficient conditions for robust closed-loop stability of a class of dynamic matrix control (DMC) systems are presented, where the l 1 norm is used in the objective function of the on-line optimization, resulting in a linear programming problem.
Abstract: Sufficient conditions for robust closed-loop stability of a class of dynamic matrix control (DMC) systems are presented. The l1-norm is used in the objective function of the on-line optimization, thus resulting in a linear programming problem. The ideas of this work, however, are expandable to other DMC-type controllers. The keys to the stability conditions are: to use an end-condition in the moving horizon on-line optimization; to have coefficients of the move suppression term in the objective function of the on-line optimization satisfy certain inequalities; and to express the uncertainty as deviations in the unit pulse response coefficients of the nominal plant. These deviations and disturbances must also satisfy certain inequalities. An off-line tuning procedure for robust stability and performance of a class of DMC controllers is also included, which determines an optimal moving horizon length and optimal values for coefficients of the move suppression term. The applicability of our approach is elucidated through numerical simulations.

Journal ArticleDOI
TL;DR: In this paper, a phenomenological, pore-scale, hydrodynamic model is developed for representation of the uniform, cocurrent, two-phase flow in the low interaction regime in trickle bed reactors.
Abstract: A phenomenological, pore-scale, hydrodynamic model is developed for representation of the uniform, cocurrent, two-phase flow in the low interaction regime in trickle bed reactors. Comparison of model predictions with numerous pressure drop and liquid holdup data reveals that phase interaction terms are negligible which results in a simplified model with no adjustable parameters. This model yields improved pressure drop and liquid holdup estimates for the low interaction regime. In addition, a criterion for the prediction of the trickle to pulsing flow regime transition is developed based on Kapitza's (1945) work on laminar film stability. This criterion compares favorably to data and to some other existing models for prediction of the trickle to pulsing flow regime transition.

Journal ArticleDOI
TL;DR: In this article, a mathematical model is developed that predicts three-dimensional, two-phase flow, heat transfer and reaction inside catalytic cracking riser-type reactors, which can predict the most important engineering aspects of a riser reactor including pressure drop, catalyst holdup, interphase slip velocity, catalyst acceleration zone, choking behavior and temperature distribution in both phases, and yields distribution all over the reactor.
Abstract: A mathematical model is developed that predicts three-dimensional, two-phaseflow, heat transfer and reaction inside catalytic cracking riser-type reactors. The model consists of the full set of partial-differential equations that describe the conservation of mass, momentum, energy and chemical species for both phases in the reactor, coupled with empirical correlations concerning interphase friction, interphase heat-transfer and fluid-to- wall frictional forces. The cracking reaction is simulated by a simple three-lump kinetic model, but more realistic kinetic models can be easily included. The model can predict the most important engineering aspects of a riser reactor including pressure drop, catalyst holdup, interphase slip velocity, catalyst acceleration zone, choking behavior and temperature distribution in both phases, and yields distribution all over the reactor. It can also predict other complex engineering three-dimensional, two-phase problems realistically using computational fluid dynamics techniques.

Journal ArticleDOI
TL;DR: In this paper, the laminar and turbulent flow behaviors of unstable and stabilised water-in-oil emulsions are reviewed. But the results of the analysis are limited.
Abstract: The literature available on pipeline flow behavior of emulsions is reviewed critically. New results concerning the laminar and turbulent flow behaviors of unstable (without any added surfactant) and surfactant-stabilized water-in-oil emulsions are presented. The unstable emulsions exhibit drag reduction behavior in turbulent flow; the measured friction factors fall well below the values expected on the basis of the laminar flow properties. Unstable water-in-oil emulsions exhibit much stronger drag reduction activity than the unstable oil-in-water emulsions. The drag reduction activity diminishes (in some cases vanishes completely) upon the addition of a surfactant to the system.

Journal ArticleDOI
TL;DR: In this paper, the authors use a supercritical fluid chromatographic technique to acquire a database of cosolvent effects for a variety of cosolsvents and solutes, showing evidence of hydrogen bonding, charge transfer complex formation and dipole-dipole coupling between solutes and cosolvents.
Abstract: The addition of cosolvents to supercritical fluid (SCF) solvents can have large effects on solubilities, giving engineers the ability to tailor loadings and selectivities of solutes for difficult separations. It is necessary to have a better understanding of the special intermolecular interactions that occur in SCF solutions to predict the effects of cosolvents. The authors use a SCF chromatographic technique to acquire a database of cosolvent effects for a variety of cosolvents and solutes; examination of the cosolvent effects shows evidence of hydrogen bonding, charge transfer complex formation, and dipole-dipole coupling between solute and cosolvent molecules. SCF solvents, carbon dioxide, ethane, and fluoroform, are compared, and then the use of the chromatograph to measure solubilities is discussed.

Journal ArticleDOI
TL;DR: In this article, an instability analysis has been carried out to elucidate the unsteady flow conditions encountered in the typical circulating fluidized bed units in light of the conveyor-solids feeder interaction.
Abstract: An instability analysis has been carried out to elucidate the unsteady flow conditions encountered in the typical circulating fluidized bed units in light of the conveyor-solids feeder interaction The results successfully predict the critical velocity and the maximum solids circulation rates reported in the literature and explain the origin of such unstable conditions Furthermore, the simulation, for the first time, reveals the importance of unit structure in improving the performance of circulating fluidized bed systems Finally, the concept of a high-density circulating fluidized bed is proposed

Journal ArticleDOI
TL;DR: In this article, the porosity development during steam activation of tire pyrolysis char is similar to that reported for various other chars, suggesting that the activation process consists of micropore formation, followed by pore enlargement.
Abstract: The primary objective of this work was to demonstrate the conversion of scrap tires to activated carbon. The authors have been successful in this endeavor, producing carbons with surface areas greater than 500 m[sup 2]/g and significant micropore volumes. Tire shreddings were pyrolyzed in batch reactors, and the pyrolysis chars activated by reaction with superheated steam. Solid products of pyrolysis and activation were studied with nitrogen adsorption techniques. They find that the porosity development during steam activation of tire pyrolysis char is similar to that reported for various other chars. A maximum in micropore volume is observed as a function of conversion, but the total surface area increases monotonically with conversion. They suggest that the activation process consists of micropore formation, followed by pore enlargement. The process conditions used in this study are a good starting point from which to optimize a process to convert tires to activated carbon.

Journal ArticleDOI
TL;DR: In this article, the authors describe how simple distillation boundaries can be crossed in continuous columns for certain ranges of the design variables, and they describe how these can be used to define additional restrictions on the product compositions.
Abstract: The product compositions in single-feed distillation columns can be specified only in certain regions of the composition space, which depend only on the pressure, feed, and vapor-liquid equilibrium for the mixture. In nonideal mixtures, even without azeotropes, the regions may allow unusual product distributions. For example, the distillate in a direct split is composed primarily of the lightest component. Intuition and experience with relatively ideal mixtures suggest that the next most plentiful component is the intermediate boiler. In nonideal mixtures, however, with or without azeotropes, the next most plentiful component may be the highest-boiling species with only trace amounts of the intermediate boiler. For azeotropic mixtures, distillation boundaries may give rise to additional restrictions on the product compositions. The authors describe how simple distillation boundaries deform into continuous distillation boundaries and, in a limited number of cases, how the simple distillation boundaries can be crossed in continuous columns for certain ranges of the design variables. Unfortunately, such designs may be quite sensitive to model uncertainties or to disturbances in the parameters.

Journal ArticleDOI
Abstract: Control structure (strategy) selection consists of the selection and pairing of manipulated and measured variables. This article outlines a procedure that uses such tools as the existence of right half plane (RHP) transmission zeros, the relative gain array, the performance relative gain array, and the closed-loop disturbance gain. The regulatory control system for the fluid catalytic cracking process is used as an example. Several authors found the Kurihara control structure to be preferable to the conventional control structure. The reason is that RHP transmission zeros limit the achievable bandwidth for the conventional control structure. Two other control structures, however, have better controllability characteristics than both the conventional and the Kurihara control structures. The sensitivity of the measurement selection and variable pairing with respect to changes in the operating point and parametric uncertainty is examined, as well as the general objectives of the regulatory control level and its interaction with the higher levels in the control hierarchy.

Journal ArticleDOI
TL;DR: In this paper, a simple model for cross-flow filtration of liquid suspensions was formulated on the premise that among the particles convected to the filter medium surface, only a fraction of them become deposited, based on the interplay of the geometry of the cake-suspension interface and various forces acting on a particle as it moves toward the interface.
Abstract: A simple model presented for cross-flow filtration of liquid suspensions was formulated on the premise that among the particles convected to the filter medium surface in cross-flow filtration, only a fraction of them become deposited. A criterion based on the interplay of the geometry of the cake-suspension interface and various forces acting on a particle as it moves toward the interface was established and an expression of the adhesion probability of impacting particles developed. The model was then formulated by incorporating the adhesion probability information together with conventional cake filtration theories. Through sample calculations, the model was found to display behavior consistent with the observed phenomena of cross-flow filtration and capable of representing experimental results.

Journal ArticleDOI
TL;DR: In this paper, a simple frictional model of this contribution to the stress is introduced, and the resulting theory is shown to predict fully developed flows with the qualitative features to be expected, even in horizontal ducts.
Abstract: Earlier work of Sinclair and Jackson on the flow of gas-particle suspensions in vertical pipes is extended to the case of ducts of arbitrary inclination. As a result of the compaction due to gravity, it is necessary to take into account forces transmitted between particles at points of sustained, rolling and sliding contact, and a simple frictional model of this contribution to the stress is introduced. The resulting theory is shown to predict fully developed flows with the qualitative features to be expected, even in horizontal ducts. The effects of flow rates, duct inclination, and duct width on the solution are explored.

Journal ArticleDOI
TL;DR: A mathematical model for quantitative prediction of wax deposition for each hydrocarbon component has been developed in this paper, where each component is characterized by weight fraction, heat of fusion, and melting point temperature.
Abstract: Deposition of wax on the wall of oil pipelines is often regarded as a problem since the tube diameter is reduced. Consequently, more power is needed to force the same amount of oil through the system. A mathematical model for quantitative prediction of wax deposition for each hydrocarbon component has been developed. Each component is characterized by weight fraction, heat of fusion, and melting point temperature. A model explains how a phase transition in the flow from liquid oil to waxy crystals may create a local density gradient and mass flux, which depends on the local temperature gradient. The model predicts that wax deposition can be considerably reduced even when the wall temperature is below the wax appearance point, provided the liquid/solid phase transition, expressed by the change in moles of liquid with temperature, is small at the wall temperature. Deposition as function of time has been obtained as a solution of differential equations derived from the principles of mass and energy conservation and the laws of diffusion.

Journal ArticleDOI
TL;DR: In this article, 2-Chlorophenol (2CP) was oxidized in near-critical and supercritical water in a high-pressure plug-flow reactor, and the global kinetics for 2CP disappearance were described by a rate law that was 0.88±0.06 order in 2CP, 0.41± 0.12 order in O2, and 0.34±
Abstract: 2-Chlorophenol (2CP) was oxidized in near-critical and supercritical water in a high-pressure plug-flow reactor. The global kinetics for 2CP disappearance were described by a rate law that was 0.88±0.06 order in 2CP, 0.41±0.12 order in O2, and 0.34±0.17 order in water. The activation energy was 11.0±3.8 kcal/mol, and the Arrhenius pre-exponential factor was 102.0±1.2 M−0.63 S−1. The uncertainties represent 95% confidence intervals. The products of 2CP oxidation included CO, CO2, HCl, other chlorophenols, chlorohydroxybenzaldehydes, dichlorophenoxyphenols, dichlorobiphenols, and chlorinated dibenzodioxins and dibenzofuran. The molar yields of the organic products were determined for a set of experiments at 380°C and 278 atm. The most abundant products were 2CP dimers such as dichlorophenoxyphenols and dichlorobiphenols, and the highest yield observed for any individual product was 0.6%. Although the yields of these products were low, their selectivities were high. For example, at 3.6 s, the shortest residence time studied under these conditions, about 50% of the carbon in the 2CP that reacted appeared in 2CP dimers, 18% appeared as CO2, and the balance (32%) was presumably in single-ring and ring-opening products. A reaction pathway analysis using the Delplot methodology revealed that the evolution of products from 2CP oxidation in supercritical water was consistent with a reaction network comprising two parallel primary reactions. One primary reaction path led to dichlorophenoxyphenols and dichlorobiphenols whereas the second primary reaction led to single-ring and ring-opening products. The 2CP dimers were convereted to single-ring and ring-opening products, which were, in turn, ultimately oxidized to CO2.

Journal ArticleDOI
TL;DR: In this article, the authors examined the mechanism by which slugs form in a stratified flow in a horizontal 0.095m pipeline at atmospheric pressure and found that at superficial gas velocities less than 3 m/s, the slugs are found to evolve from waves, with a length of about 0.085 m, that are generated by a Jeffreys mechanism.
Abstract: Experiments were conducted with air-water flow in a horizontal 0.095-m pipeline at atmospheric pressure to examine the mechanism by which slugs form in a stratified flow. A specially designed entrance box was used to avoid disturbances. In these experiments, at superficial gas velocities less than 3 m/s, the slugs are found to evolve from waves, with a length of about 0.085 m, that are generated by a Jeffreys mechanism. These waves grow in height and eventually double in wavelength by a nonlinear resonance mechanism. Depending on the height of the liquid, the growth can lead to a breaking wave or to a wave that fills the whole pipe cross section. At superficial gas velocities equal to or greater than 4 m/s capillary-gravity waves with a wide range of lengths are generated by a linear Kelvin-Helmholtz mechanism. These rapidly evolve into long waves outside the range of linear instability. If the liquid height is large enough, these waves can form slugs through a nonlinear Kelvin-Helmholtz instability that is aided by wave coalescence.

Journal ArticleDOI
TL;DR: In this article, the authors studied the influence of CO and NO on the formation of N2O in a quartz flow reactor in the presence of CO, NO and other gases.
Abstract: N2O decomposition and formation during the oxidation of NH3 and HCN were studied in a quartz flow reactor in the presence of CO, NO and other gases. The emphasis is on the influence of CO and NO. In addition, the homogeneous nitrogen chemistry of fluidized bed combustion and the selective noncatalytic reduction of NO (SNR) are discussed. The rate of N2O decomposition in N2 agrees with a first-order rate expression. The presence of CO or H2 increases the decomposition rate regardless of the additional presence of O2 For the formation of N2O, HCN oxidation is more efficient than NH3 oxidation. The presence of NO increases the amount of N2O formed during the oxidation of HCN or NH3.CO moves the N2O formation toward lower temperatures. H2O increases the reaction rate where few components are present, whereas H2O has little influence in the presence of large amounts of a combustible component such as CO. There are indications that NO is a necessary intermediate for any significant formation of N2O during the oxidation of NH3 and HCN. NO reduction is obtained when NO is initially present during oxidation of both NH3 and HCN. These results are comparable to the respective SNR results with reductant ammonia and urea.

Journal ArticleDOI
TL;DR: In this article, the nitrogen hyperfine splitting constant of ditertbutyl nitroxide radicals was measured with electron paramagnetic resonance spectroscopy at near-infinite dilution in near-critical and supercritical ethane, as well as in liquid propane, liquid isobutane, and several nonhydrogen bonding liquid solvents.
Abstract: The nitrogen hyperfine splitting constant of ditertbutyl nitroxide radicals was measured with electron paramagnetic resonance spectroscopy at near-infinite dilution in near-critical and supercritical ethane, as well as in liquid propane, liquid isobutane, and several nonhydrogen bonding liquid solvents. While the measurements in the liquids are described well by the theory of McRae, large deviations from the liquid behavior are observed in supercritical ethane. The deviations are used as a measure of the effective local density of the solvent around the solute. At the two temperatures investigated, Tr = 1.009 and Tr = 1.084, the local density enhancement, defined as the ratio of local to bulk densities, exhibits a maximum of about 3 occurring around 1/2 the critical density. The maximum is removed well from the critical density, where the maximum of the isothermal compressibility is observed. Local density enhancements are short-range effects and do not correlate well with the development of long-range critical phenomena. Local density enhancement data in ethane are compared with the prewetting transition that has been observed in nearcritical ultrapure argon.