stants were available. A smooth curve results but the physicochemical significance is not obvious.
CONCLUSIONSSeveral nonprotogenic solvents for sucrose have been found.The solubilities can be expressed by straight lines characterized by two parameters, one depending on the nature of solvent, the other on the nature of dissolved material. Even with the few results given it would appear that only the solubility of sucrose at one temperature and the dielectric constant of the solvent are required to predict the solubility at any other temperature.Many further measurements are needed in order to determine the parameters more accurately and to find whether this rule can be applied to other substances than sucrose.
Wel, J.; Denn, M. M. A I C M J . 1978a, 24, 885. Yoon. H.; Wel, J.; Denn, M. M. AIChE J . 1978b. 25, 429. t = time At = time increment T = temperature of gas stream { = temperature of solid stream T, = wall temperature U = gas-wall heat transfer coefficient z = distance from bottom of the reactor Greek Symbols a number of hydrogen atoms per carbon atom in char 6 = number of oxygen atoms per carbon atom in char y = stoichiometric coefficient of oxygen in char-oxygen reactionLocal models are used to represent equilibrium ratios (K values) essential to the design of separation processes.These simpllfied models are derived from the rigorous thermodynamic relationships that govern phase equilibria. The local models provide an Interface between the design algorithm and real data or an extensive library of thermophysicai property subroutines used for rigorous property evaluations. The models have been developed for both multicomponent vapor-liquid and IiquM-liquid systems. During any computational procedure in which the iocai models are used, parameters In the models are periodically updated by recursive use of the thermophysicai property data base. This ensures that an accurate representation of phase equilibria is maintained at all times at a cost significantly less than by the use of rigorous thermodynamic property evaluations alone.
Simple, local models are used in a two-tier structure for incorporating thermodynamic and physical properties into dynamic process calculations. To maintain the accuracy of the approximated models as the process conditions vary, the parameters in the local models are adjusted periodically by using the rigorously calculated property values and a recursive, least-squares update. The sampling time for the rigorous evaluations is variable and is selected automatically. The resulting algorithms yield a substantial reduction in the number of rigorous evaluations and associated computer time. Examples are presented for the dynamic simulation of small-scale, vapor-liquid equilibrium problems.The problem of efficiently incorporating thermodynamic and physical (TP) properties in process design calculations was considered in the first two parts of this series (Chimowitz et d., 1983(Chimowitz et d., ,1984. Several fundamental concepts and a number of applications to typical design problems were presented there. Those basic ideas can be summarized as follows:1. Simple ("local") models are considered which approximate locally more rigorous and expensive TP property models. The local models contain adjustable parameters so that they can be fit to a particular region in the temperature, pressure, and composition space.
2.A given design or simulation problem is reformulated in terms of the local models. This produces a more manageable mathematical problem whose solution becomes easier and more economical.3. Since the local models, by their very definition, do not have global validity, using them outside of the region where the parameters were fit may result in some inaccuracy. However, the model parameters can be recalculated ("updated") in the new region. This procedure is repeated until the problem is solved.These ideas resulted in a solution procedure, two-tier in structure (Rosen, 1980), which is schematically represented in Figure 1 and which we named the P-DELTA method. P-DELTA is an acronym for Process DEsign by Limiting Thermodynamic Approximations. An important advantage of this two-tier structure is the decoupling of the thermodynamic package (data base and rigorous TP estimation routines) from the process solution procedure.In the first paper (part l), local models were developed to represent distribution coefficients ( K values) in vapor-liquid and ternary liquid-liquid systems. Several simplifications, based on pseudobinary interactions between the components of a mixture, led to compositiondependent local models which can accurately represent ideal and nonideal solutions, including azeotropic mixtures. Typical local models are shown in Scheme I. The second paper (part 2) illustrated the application of local models to fundamental problems in separation processes such as University of Rochester, Rochester, NY 14627. Scheme I. Typical Local Models for Vapor-Liquid K Values" In (Ki.P) = ai + bi In f r o In (Ki.P) = ai + bi In f i a + ci(1 -xi)'In all models, f" is the standard-state fugacity (at zero pressure and syste...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.