This review aims to provide both an outline of the fundamental concepts and a review of the most recent developments in phase transition and equilibrium. Small molecule, polymer and gel systems all fall within its scope, with particular reference being made to phase-equilibrium patterns, prediction of equilibrium properties and the kinetics of phase transition. An attempt is made to explain the particular phenomena involved in these systems and the similarities between them by reference to the concept of the connectivity of molecular chains.
The Luenberger observer design method is extended by a further interesting consideration. This paper addresses the design method of robust observers for linear systems with uncertainty and a class of nonlinear systems by applying the concept of system roubstness degree proposed by the authors. The uncertainty in linear systems and nonlinear distortion in nonlinear systems may lead the observer to be unstable. The Luenberger observer design approach combined with the system robustness degree will construct a robust asymptotic observer. Reduced-order robust observer design is also studied. Finally, a practical example of nonlinear robust observer design for a biochemical reactor is illustrated to show the validity of the proposed method.
A two-dimensional riser with transparent walls has been successfully operated in a CFB loop. Solids flow structures have been investigated through the glass front wall by means of a motion analysis system. Slugs and gas-percolated plugs are observed in the dense and dilute regions of the riser respectively. Particle aggregates in the riser have elongated shapes and are not dispersed but are structured as solids streaks flowing in converging and diverging branches. The latter appear like small slugs extending on a fraction of the riser width only.
Particle behavior in a horizontal gas-solid agitated vessel with two parallel axes was investigated. The particle behavior depends on the particle holdup and flow velocity as well as their distribution in the vessel. Therefore particle holdup and three components of particle velocity were quantitatively measured at a local point in the vessel by using an electrostatic-capacity method and an image-sensor technique, respectively. A model based on the balance of the forces which act on a particle was also proposed to estimate the particle trajectory in the vessel. This model enabled us to predict the elevation of particle through the particle trajectory and velocity. The particle velocity calculated by this model was almost in agreement with the measured maximum velocity.
A continuous flow electrophoretic process for the concentration of amino acid has been modeled on the basis of a transport equation including ionic migration and dissociation reaction between the ions. The model equations were solved as an initial value problem by using a finite-difference technique. Experiments on concentration of amino acid were also performed to ascertain the validity of the mathematical model and the numerical method used to solve the model equations. Experimental results for the degree of concentration of amino acid and pH distribution were in fair agreement with theoretical results, indicating that the model and numerical method are valid. Further, the effect of applied voltage and background electrolyte concentration on the process of concentrating amino acid was studied on the basis of numerical simulation under various conditions. The results obtained show that there exist a dynamic equilibrium and limit of concentration for amino acid.
Experimental data on the effects of operating conditions such as pH, particle diameter, concentration of limestone, presence of dissolved iron ions, and species of sparged gases on the neutralization rates of acid waters containing metal ions by limestone have been obtained and investigated from thermodynamic and kinetic points of view. The concentrations of dissolved ions in the solution at a given pH and the rates of dissolution are explained respectively by an equilibrium model and a model based on an instantaneous reversible reaction of calcite and hydrogen ion. This rate model shows good agreement with the experimental data.
A dynamic model of a fixed bed reactor with catalyst deactivation was developed for on-line optimization and control system design. First, the kinetic equations for the reaction of carbon dioxide with methane over a nickel catalyst are determined by experiments under negligible deactivation. Deactivating factors are then introduced to evaluate the effect of catalyst deactivation on actual reactor performance. Under some assumptions, a lumped-parameter model is represented by nonlinear ordinary differential equations (NODEs) from the energy and mass balances. By linearizing the NODEs the transfer function, which is convenient for designing a control system, is obtained. Both the models of NODEs and the transfer function are used for simulation of the temperature control system. The results agreed well with experimental data under two typical catalyst conditions.
A design method was proposed for the fixed-gain feedback controller which is sufficiently robust under the variations of process dynamics. The variations or uncertainties in the process dynamics are represented by variations of uncertain parameters in the process model. For each typical operational condition the region of possible variation is approximated by an orthotope. This orthotope is the required region of tolerance. On the other hand, the region of uncertain parameters, in which the control system has admissible system performance, is the inherent region of system tolerance. The controller is designed so that the inherent region of tolerance contains the required region of tolerance. The design algorithm is composed of the iteration of two steps: a robustness test for the proposed design and a controller parameter retuning for the required tolerance. The method was applied successfully to processes for which the dynamics depends on the throughput.
The extraction of palladium by didodecylmonothiophosphoric acid is carried out, using a highly stirred tank and a stirred transfer cell to clarify the extraction mechanism. Measurements of palladium-loading capacity and of interfacial adsorption equilibrium of the extractant are also conducted. The dependency of the extraction rate on the concentration of the chemical species taking part in the extraction is examined. An interfacial reaction model in which four chloro-palladium complexes take part is proposed. The experimental results are analyzed by the model to obtain the reaction rate constants of these four complexes with the extractant. The order of magnitude of the reaction rate constants is explained qualitatively by the trans-effect.
The natural and Marangoni convections formed spontaneously in the melt inside a two-dimensional rectangular open boat were investigated by means of an order-of-magnitude evaluation and a numerical analysis according to the finite difference method. A quantitative evaluation was made of the Grashof number, Marangoni number, Prandtl number and melt depth, all of which affect the interfacial velocity and the velocity distribution of the melt convection. It was concluded that Marangoni convection as well as natural convection is important when the melt is shallow.
A hybridoma cell line epo2C which produces anti-erythropoietin monoclonal antibody was immobilized with alginate and urethane polymer under several conditions. Concentration of the alginate affected neither the cell growth nor the antibody production when the alginate was hardened by calcium. However, the concentration was very important when strontium was used for the hardening. By coating alginate gel with urethane polymer, a long term cultivation of the immobilized cells and stable antibody production by a fluidized bed reactor were possible without destruction of the gel particles. During the cultures, the cells leaked from the alginate gel but were trapped inside of urethane coat with any types of gel. Therefore, high cell density of more than 107 cells/cm3-gel was attained and volumetric productivity of the antibody was 0.8 mg/(cm3·d). This method will provide a promising way for effective and simple antibody production.
The effect of the nickel concentration profile on the selectivity of acetylene hydrogenation was investigated by using nickel/alumina catalysts with different concentration profiles: egg shell of thin layer, egg shell of thick layer, uniform, and egg yolk. A model calculation of selectivity was also carried out. The selectivity of ethylene showed the following order: egg shell of thin layer > egg shell of thick layer > uniform > egg yolk. The result of the model calculation showed comparatively good agreement with the experimental results.
A mathematical model of heat and mass transfer for the rotating evaporator surface on a centrifugal molecular still has been developed for binary mixtures. A numerical solution for the relationship between the rate of distillate and its composition and an approximate solution under a special condition are proposed, and effects of some dimensionless parameters on the evaporation phenomena are discussed. The validity of this mathematical model was demonstrated by evaporation experiments for two binary systems; DBP (dibutyl phthalate)-EHP (di-2-ethylhexyl phthalate) and EHP-EHS (di-2-ethylhexyl sebacate), using two centrifugal molecular stills. Experimental data agreed well with the numerical solution and the usefulness of the mathematical model was elucidated.
Among the various residue upgrading processes in use, conventional hydrodesulfurization (HDS) units operated at elevated temperatures are widely employed for cracking of inferior crudes with a high metal content, such as Middle East or South American crude. Such a high-temperature operation results in inducing dry sludge formation in product oil and maximum conversion is regulated by that limitation. With a combination of hydrovisbreaking and hydroconversion by asphaltene bottom cracking (ABC) catalyst the maximum conversion was improved by as much as 15% for inferior crudes. The advantage of the higher conversion was proved by characterizing the reaction mechanism in the process. And, the reaction mechanism model and prediction model for compatibility of product oil proposed for the prediction of maximum conversion will also be a tool for optimizing various types of residual hydroconversion processes.
A practical model of the thermal cracking of residual oil was developed. It is basically a lumping model stating reactions of hypothetical components, commonly used in petroleum refining reactions. Four lumped components were defined to represent polymerization and condensation of residue as a minimum requirement. Cracked product was arbitrarily divided into four lumps. Introduction of the atmospheric equivalent temperature to rate constants in the Arrhenius form made quantative descriptions of the effect of phase equilibrium states in the reactor on the reaction rate distinctively clear. Incorporating the residence-time distributions, the model predicted the performance of various types of thermal cracking reactors such as batch, semi-batch and CSTR (complete stirred-tank reactor), not only in laboratory experiments but also in commercial operation.