Correction factors for the dynamic measurement of the volumetric mass-transfer coefficient

The experimental determination of the volumetric mass-transfer coefficient based on the use of an oxygen electrode requires a mathematical model of the experimental system and a parameter estimation method to obtain a number for the k_ta value. Previous work has resulted in a number of different model structures corresponding to different hypotheses concerning the relevant physical phenomena. Little is known about the impact of a specific choice for the model structure or that of the estimation procedure on the numerical value of the mass-transfer estimate. This impact is investigated here and guidelines are given for the choice of a parameter estimation scheme. In addition, correction factors that measure the impact of a structural choice are given for both the moment and least squares parameter estimation methods. The diagrams may be used in a preliminary phase to make an overall appraisal of the specific experimental conditions and in the estimation phase to reduce computational loads.     

Equation of State of Explosion Products on the Basis of a Modified Van der Waals Model

A semi-empirical model is proposed for the equation of state of high explosives in a range of pressures and temperatures typical of detonation processes. A possibility of formation of solid phases (e.g., graphite or diamond) in the gas is implied. The model can be used to calculate all thermodynamic quantities for arbitrary molecular compositions and to calculate the thermodynamically equilibrium molecular (and phase) composition. An iterative scheme of calculations is proposed. The model contains several empirical functions whose form can be changed without violating the overall calculation scheme. A particular set of these functions is considered as an illustration. Some results calculated for a number of high explosives containing four elements (C, H, N, and O) are presented. The calculated results are compared with available experimental data. __________ Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 1, pp. 87–99, January–February, 2006.     

Thermodynamic modeling of liquid crystal-nonmesogen systems in the approximation of the theory of regular solutions

Nematic (or smectic-nematic) liquid crystal-nonmesogen systems are investigated by thermal analysis methods. A method for predicting the T-x diagrams of these systems using a model of regular solutions is proposed. The method gives good agreement between the predicted and experimental data in determining the phase separation in a system and calculating solubility polytherms. Specific features of calculation of the solubility parameter of liquid-crystal compounds are considered.     

Modification of the Phase Composition of Glass Batch in Granulation

Phase transformations in glass batches in densification are analyzed. A method for the calculation and construction of phase diagrams is proposed that provides a clear representation of the qualitative and quantitative phase modifications related to the physicochemical processes occurring in the glass batch at particular stages of granule formations and makes it possible to actively control these processes for the purpose of obtaining products with prescribed technological properties. __________ Translated from Steklo i Keramika, No. 8, pp. 6 – 9, August, 2005.     

Classification of global fluid-phase equilibrium behaviors in binary systems

The study of phase equilibria is one of the most important sources of information about the nature of intermolecular forces in liquids and their mixtures and is of the highest importance for designing and optimizing processes. Many of the main features of vapor–liquid and liquid–liquid phase behavior were well characterized experimentally during the early part of the 20th century, and many equations of state were developed to reproduce the many types of phase diagrams observed for binary systems. In spite of the quasi-infinite number of possible configurations and rearrangements of fluid–fluid equilibrium phase diagrams, this paper presents a near-exhaustive classification scheme of fluid phase equilibria in binary systems. It starts from the one proposed by Van Konynenburg and Scott and brings it up-to-date by detailing the progress carried out on this topic since their classification scheme was first proposed. The second part of this paper is devoted to describing the transitions between the various types of systems.     

Prediction and quality control of the melt index during production of high-density polyethylene

In polyolefin processes the melt index (MI) is the most important control variable indicating product quality. Because of the difficulty in the on-line measurement of MI, a lot of MI estimation and correlation methods have been proposed. In this work a new dynamic MI estimation scheme is developed based on system identification techniques. The empirical MI estimation equation proposed in the present study is derived from the 1 ^st -order dynamic models. Effectiveness of the present estimation scheme was illustrated by numerical simulations based on plant operation data including grade change operations in high density polyethylene (HDPE) processes. From the comparisons with other estimation methods it was found that the proposed estimation scheme showed better performance in MI predictions. The virtual sensor model developed based on the estimation scheme was combined with the virtual on-line analyzer (VOA) to give a quality control system to be implemented in the actual HDPE plant. From the application of the present control system, significant reduction of transition time and the amount of off-spec during grade changes was achieved     

Modelling of a dynamic multiphase flash: the positive flash: Application to the calculation of ternary diagrams

A general and polyvalent model for the dynamic simulation of a vapor, liquid, liquid–liquid, vapor–liquid or vapor–liquid–liquid stage is proposed. This model is based on the τ-method introduced as a minimization problem by [Comput. Chem. Eng. 22 (7/8) (1998) 897] for steady-state simulation. They suggested modifying the mole fraction summation such that the same set of governing equations becomes valid for all phase regions. Thanks to judicious additional switch equations, the τ-formulation is extended to dynamic simulation and the minimization problem is transformed into a set of differential algebraic equations (DAE). Validation of the model consists in testing its capacity to overcome phase number changes and to be able to solve several problems with the same set of equations: calculation of heterogeneous residue curves, azeotropic points and distillation boundaries in ternary diagrams.     

Simulation of phase diagrams of oxychromites with a spinel structure

Phase diagrams of oxychromites with a spinel structure are described in the context of the Landau phenomenological theory of phase transitions. As an approximation of the thermodynamic potential of the sixth degree with respect to components of the order parameter, the implementation conditions of each type of phase diagrams are found. Equations for calculation of coordinates of tricritical and triple points are obtained. A qualitative agreement of the theoretically calculated results of the phase diagrams and experimental phase diagrams of some oxychromites with a spinel structure is observed.     

Global analysis of the multiplicity features of multi-reaction lumped-parameter systems

Mathematical models of lumped-parameter systems in which many chemical reactions occur simultaneously contain a large number of parameters, so that a p Theoretical guidance is needed to determine all the multiplicity features and the corresponding parameter regions.A systematic, efficient scheme is presented for finding parameter values corresponding to a specific number of solutions. A new scheme is developed for bifurcation diagrams, which describe the dependence of a state variable on a slowly changing operating variable. Some general predictions are made abou systems. Bounds on the values of the bifurcation or state variable may create bifurcation diagrams which cannot be found close to the highest order sin of solutions even when an isola variety does not exist. Several examples illustrate the application of the mathematical techniques.     

Ternary hydrogen-bonded polymer solutions

Ternary-phase diagrams have been experimentally determined at 100°C for systems containing a series of poly(n-alkyl methacrylates), poly(ethylene oxide) (PEO), and a solvent [4-ethyl phenol (EPh)]. A totally miscible phase diagram is experimentally determined for the poly(methyl methacrylate)/PEO/EPh system, while a closed-loop diagram is observed for the analogous system containing poly(ethyl methacrylate). The corresponding phase diagrams of analogous mixtures containing poly(n-propyl methacrylate) or poly(n-butyl methacrylate) exhibit large heterogeneous areas. Theoretically predicted phase diagrams calculated using an association model developed in our laboratory are in general accord with these observations for ternary hydrogen-bonded polymer/polymer solutions. © 1998 John Wiley & Sons, Inc. J. Appl. Polym. Sci. 70: 1265–1271, 1998     

Counter-current solid liquid extraction in a cascade of batch extractors

An analytical solution and method of calculation is presented for a cascade of N perfectly mixed batch extractors operating counter-currently, for spherical solid particles, with parameters which may vary for each extractor. The results for the case of constant and equal parameters along the complete cascade are presented in dimensionless plots; N varies from 1 through 10. The practical interest of these diagrams lies in their use in design and/or in foreseeing the behavior of a cascade when its parameters undergo variations. A sample calculation is included.     

Thermodynamic Model for Prediction of Phase Equilibria of Clathrate Hydrates in the Presence of Water-Insoluble Organic Compounds

A thermodynamic model for the prediction of pressure–temperature phase diagrams of structures II and H clathrate hydrates of methane, carbon dioxide, or hydrogen sulfide in the presence of “water-insoluble” organic componds is presented. The model is based on the equality of water fugacity in the aqueous and hydrate phases. The solid solution theory of van der Waals–Platteeuw (vdW–P) is used for calculation of the fugacity of water in the hydrate phase. The Peng–Robinson (PR) equation of state (EoS) is employed to calculate the fugacity of the components in the gas phase. It is assumed that the gas phase is water and promoter free and the organic compounds do not have marked effects on water activity in the aqueous phase. The results of this model are compared to existing experimental data from the literature. Acceptable agreement is found between the model predictions and the investigated experimental data.     

An adaptive refined grid search strategy for assessing operational flexibility and application on refrigerant selection

A novel adaptive refined grid search strategy is developed for representative characterization of process feasible region boundaries and accurate estimation of its hypervolume. In particular, a linked list data structure adopted from the field of computer science is used to maintain the grid connectivity information. A uniform perturbation scheme is used to refine the search only near the boundaries. The volumetric flexibility index (FI_V) is calculated directly from a summation of feasible hypercubes in the grid, without the need to apply shape reconstruction techniques. The proposed adaptive grid search strategy can capture complex region shapes with reduced sampling costs and without randomness, increasing reproducibility. Operational flexibility is optimized traditionally at a process scale. A case study on refrigerant selection is presented to demonstrate that the developed strategy can be combined within a computer-aided molecular design framework for operational flexibility optimization at the molecular scale.     

A simple,reliable and fast algorithm for the simulation of multicomponent distillation columns

This work has developed a simple, reliable and fast algorithm for the simulation of multicomponent distillation columns, where any equilibrium stage can accept a feed-stream and/or a vapor-side-stream and/or liquid-side-stream. The new scheme considers internal molar overflows and constant relative volatilities to avoid the need of heat balances and vapor–liquid equilibrium calculations. The solution scheme is founded on a Newton-based formulation in block algebra, which relies in a simple, reliable and fast algorithm. Although the proposed calculation scheme can be classified as an approximate method, it is very useful when accurate phase equilibrium and enthalpy data are lacking. Numerical experimentations show good agreement with the results obtained with well-known rigorous simulation approaches.     

Phase structure coarsening in polymer blends: predicted effects of the phase duality interval on selected physical properties

A predictive scheme for simultaneous evaluation of the modulus, yield (or tensile) strength and gas permeability of heterogeneous polymer blends is used to estimate the effects of the phase duality interval delimited by the critical volume fractions of components v_1cr and v_2cr. The scheme combines a two‐parameter equivalent box model and the data on the phase continuity rendered by modified equations of the percolation theory. In addition to respective properties of constituents, the scheme also takes into account interfacial adhesion either sufficient or insufficient for stress transfer at yielding (or fracture). Simultaneously predicted properties of a blend are inter‐related through an identical set of input parameters characterizing a specific phase structure. It is schematically shown for model blends that narrowing of the phase duality interval due to phase structure coarsening accounts for a noticeable decrease in considered properties, particularly in yield (or tensile) strength if the interfacial adhesion is insufficient for the transfer of acting stress.     

Assessment of the CaO-Al2O3 System

A thermodynamic assessment of the quasi-binary system CaO-Al₂O₃ has been made using a computerized CALPHAD (calculation of phase diagrams) technique. The actual optimization was carried out with a computer program for the optimization of parameters in thermodynamic models called PARROT. The liquid phase is described by a simple two-sublattice subregular solution model with Ca²⁺ and Al³⁺ as cationic species and O^2- as anionic species. All solid phases are treated as stoichiometric compounds. A consistent set of parameters describing the system is presented, and numerous comparisons with experimental data are made. There is a lack of accurate data in the high-alumina part of the system, and the importance of a better knowledge of the CaO·6Al₂O₃ phase is stressed.     

Computer simulation of stiff-chain polymers

A review of studies on the computer simulation of the phase behavior of various stiff-chain polymer systems is presented. Methods for calculating phase diagrams of a polymer solution in a computer experiment are discussed, including the methods of extended ensembles, entropic simulation, and the Wang-Landau algorithm to obtain the density-of-states function. The authors’ original results on studying the intramolecular orientational and spatial ordering of monomer units in a single stiff-chain macromolecule in the bulk and near a planar adsorbing surface by means of the Wang-Landau algorithm and using the bond-fluctuation lattice model are presented. Corresponding state diagrams are presented for these two cases. For systems of multiple chains, the phenomenon of nematic liquid-crystalline ordering in semi-dilute solutions in the bulk and in a planar layer is considered, and the phase diagrams for these cases are presented. A survey of the published data on some other promising directions of investigation of stiff-chain polymer systems is presented.