Isothermal (vapor + liquid) equilibria of (4-methylpentan-2-one + pyridine + 1,4-dioxane) at four temperatures
Isothermal (vapor + liquid) equilibria of (4-methylpentan-2-one + pyridine + 1,4-dioxane) have been measured at (308.65, 313.15, 318.15, and 323.15) K using the total-pressure method. The pressure was also predicted using the Wilson model with parameters determined from binary (vapor + liquid) equilibria. The predicted vapor pressures agree satisfactorily with the measured values at all four temperatures. © 1990.
Isothermal (vapour + liquid) equilibria of (tetrahydrofuran + acetonitrile + 1,2-dichloroethane)
A one-parameter model for granulation
The total population balance equation for granulation is examined when coalescence as well as crushing and layering are modes of growth. Previous solutions for the case of random coalescence are inadequate for describing a wide variety of granulating systems. A single parameter model is proposed to describe the reduced number density function of granules as a function of reduced granule size. Further, the relationship between model parameter and the empirical ballability index proposed in the literature is shown to be monotonic. The present model correlates very well the data on a wide variety of granulating systems besides providing a good approximate solution to the population balance equation. © 1982.
Excess gibbs free energy of mixing
Narayanan, K.V. and Ananth, M.S., 1993. Excess Gibbs free energy of mixing. Fluid Phase Equilibria, 91: 77-86. The statistical mechanical approach to developing excess Gibbs free energy models for liquids using lattice theories in the Canonical ensemble is reexamined numerically in the light of the fundamental observations of Sandler et al. (S.I. Sandler et al., 1989. Fluid Phase Equilibria, 45: 251-265). Calculations are carried out for mixtures of hard sphere fluids and model mixtures of Lennard-Jones (LJ) molecules to find the effect of varying the relative size of the hard sphere molecules and the unlike interaction parameters for LJ mixtures on the difference between the excess Gibbs free energy at constant pressure and the excess Helmholtz free energy under different mixing constraints. It is shown that for engineering purposes lattice theories can only provide mathematical expressions that fit mixture data accurately provided these expressions contain one or two adjustable parameters. Further, for fitting excess Gibbs free energy data it is shown that expressions for the excess Helmholtz free energy under any of the constraints ("Scatchard mixing", mixing under constant number density or constant reduced density) are equally useful. © 1993.
Parameter estimation in a fixed-bed reactor operating under unsteady state: Oxychlorination of ethylene
During the oxychlorination of ethylene, the composition of the catalyst, cupric chloride, is subject to change, and hence estimation of rate parameters considering the unsteady-state situation is more reliable than assuming steady state. In the present work, nonisothermal experimental data are collected in an unsteady-state fixed-bed reactor by changing the inlet temperature using a temperature-programmed preheater. The rate parameters are estimated by developing an unsteady-state model which takes into account not only the reaction temperature and gas-phase conversions but also changes in the solid-phase composition in the catalyst bed. The rate parameters estimated in this study are found to be different from the steady-state values reported in the literature. The disagreement in the rate parameters has been explained in terms of the properties associated with the solid phase. The most significant feature of this work is that the rate-temperature behavior, calculated using the present rate constants, corresponds closely with that derived from independent catalyst composition studies reported in the literature, thus indirectly validating the parameters estimated in this work.
On unsteady state moving boundary problems for non-plane geometries
Many models for fluid-solid non-catalytic reactions in chemical engineering involve the solution of the diffusion equation for non-plane geometries subject to a moving boundary. One of the simplest cases is that in which diffusion of the gaseous reactant through the product layer controls the overall rate of the reaction. Even in this case the moving boundary introduces a non-linearity so that few analytical solutions have been attempted. The ratio of the densities of the fluid and solid reactants, β, is an important parameter in this model. In the limit as β → 0 the equations can be solved analytically. The resulting solution, referred to as the pseudo-steady state approximation, is widely used in chemical engineering especially in the design of reactors. Perturbation solutions built around this approximation are, however, known to lead to erroneous solutions in non-plane geometries. In the method developed in this paper the curvature term is retained in the equations even in the zero order approximation. The dimensionless radial width of the ash layer is used effectively as the perturbation parameter. The resulting series solution appears to converge rapidly to the exact solution even for large values of β. It is shown, incidentally, that the pseudo-steady state solution does not provide a conservative estimate of the time of reaction. © 1992.
Modelling of hydrotreating process in a trickle-bed reactor
Pilot scale hydrotreating experiments have been conducted on straight run high speed diesel oil (SR HSDO) using commercially available Co-Mo on Al2O3 catalyst. Kinetics of hydrodesulphurization and hydrodenitrogenation are studied using the models that took into account the physical and chemical complexities of the three phase system. Correlations are developed to predict the product properties based on operating conditions. The results show a good agreement with the experimental data.
Augmented Gibbs-Tolman Model for Surface Tension
Gibbs developed the thermodynamics of a liquid-vapor system by introducing the idea of a "dividing surface" a hypothetical surface that separates the system into two homogeneous phases. The area and curvatures of a conveniently chosen dividing surface, the "surface of tension", are used to account for the effects of the smooth variation of properties across the actual transition layer between the phases. Tolman (1948, 1949) considered a more detailed model of the interfacial region and obtained expressions for surface tension (σ) and the location of the surface of tension. Based on qualitative arguments, Tolman's model introduced a surface of tension, such that the pressure (P) increases from its saturation value (Psat) to a maximum value (Pmax) as the surface is approached from the vapor side and decreases from (Psat) to its minimum value (Pmin) as the surface is approached from the liquid side. Assuming an exponential decay of (P) away from the surface, Tolman obtained an explicit expression for (σ) in terms of Psat, Pmax, Pmin, and two length scales. In the this work, the Gibbs-Tolman (GT) model is used along with the Lee and Kesler (1975) equation of state. The model is augmented to take into account the effect of the density gradient in the transition zone and a 4-parameter augmented model (AGT model) is proposed. The GT and AGT models are shown to fit the data for 152 pure liquids with an absolute average deviation (AAD) of 4.91% and 2.02%, respectively. The corresponding AAD values for 57 liquid mixtures are 4.2% and 3.0% respectively. Arguments are also presented to counter some of the fundamental concerns that have been raised about the GT approach. Although the model correlates the data very well, one of the length parameters turns out to be persistently negative, and the reason for this behavior is not clear.
Self†consistent local composition model of electrolyte solutions
A self‐consistent local composition theory for the excess Gibbs free energy of a multicomponent electrolyte solution is developed. The theory incorporates correct pair counting, assumes that like‐charged ions cannot be nearest neighbors of each other, and accounts for the effect of second nearest neighbor interactions. A perturbation analysis of the model, linear in the interaction parameters, is also carried out. For a given solvent and a given class of electrolyte the perturbed theory yields universal functions of molality, which can be weighted by suitable parameter values and added to give the desired property. The parameters can be expressed in a temperature‐independent form. This theory correlates very well the data on osmotic and activity coefficients in single‐solute aqueous solutions up to very high concentrations (up to 20 M) as well as over a range of temperatures. Copyright © 1990 American Institute of Chemical Engineers
Hydrodynamics of two†phase cocurrent downflow through packed beds. Part II: Experiment and correlations
Two‐phase pressure drop and dynamic and total liquid saturation are experimentally determined for air‐water system under cocurrent downflow through packed beds using packing differing widely in geometry. The experimental data of the present study as well as that available in literature is satisfactorily correlated in terms of: (a) Lockhart‐Martinelli parameters; and (b) the Reynolds numbers defined for the respective phases and the bed porosity, taking into account the flow behavior of the phases through the packed bed. Copyright © 1983 American Institute of Chemical Engineers