Multi-component calculations

Liddle [136] presents a shortcut technique for multi-component calculations based on improving the Fenske and Gilliland correlations. 

Step-by-Step Examples of Multi-Component Calculations 313... 

Chapter 10 provides an exhaustive description of how these techniques can be applied to a large number of industrial alloys and other materials. This includes a discussion of solution and substance databases and step-by-step examples of multi-component calculations. Validation of calculated equilibria in multi-component alloys is given by a detailed comparison with experimental results for a variety of steels, titanium- and nickel-base alloys. Further selected examples include the formation of deleterious phases, complex precipitation sequences, sensitivity factor analysis, intermetallic alloys, alloy design, slag, slag-metal and other complex chemical equilibria and nuclear applications. 

The interaction parameters derived in this way are usually concentration-dependent, making for lengthy computations. It is therefore unlikely that this route will ever be adopted for multi-component calculations unless more efficient algorithms can be developed. Apart from this aspect, the method is attractive... 

CALPHAD—A Comprehensive Guide lOJ. GENERAL BACKGROUND TO MULTI-COMPONENT CALCULATIONS... 

The understanding of the critical systems in an assessed database is in the hands of the developer of the database and can often only be understood after a series of multi-component calculations are made. 

The calculation of vapor and liquid fugacities in multi-component systems has been implemented by a set of computer programs in the form of FORTRAN IV subroutines. These are applicable to systems of up to twenty components, and operate on a thermodynamic data base including parameters for 92 compounds. The set includes subroutines for evaluation of vapor-phase fugacity... 

Equation (4) is the )cey equation for calculation of multi-component vapor-liquid equilibria. 

CHEMCALC 1, Separations Calculations Gulf Publishing Company, Book Division P.O. Box 2608 Houston, TX 77252 Programs for use with multi-component mixtures to determine the conditions and compositions at the dew point and at the bubble point. 

Yu, A.B. and Standish, N., 1987. Porosity calculations of multi-component mixtures of spherical particles. Powder Technology, 52, 233-241. 

If the values calculated in these two ways are identical, the fluorescence decay is indeed a single exponential. Otherwise, for a multi-component decay, t < tm. In this case, several series of images have to be acquired at different frequencies (at least 5 for a triple exponential decay because three lifetimes and two fractional amplitudes are to be determined), which is a challenging computational problem. 

Pandat software package and applications (Chen et al. 1993). Pandat is a software package for multi-component phase diagram calculations. Given a set of thermodynamic parameters for all phases in a system and a set of user constraints, Pandat automatically calculates the stable phase diagram without... 

UNDERWOOD, A. J. V. J. Inst. Petroleum 32 (1946) 614. Fractional distillation of multi-component mixtures — calculation of minimum reflux ratio. 

An equilibrium-flash calculation (using the same equations as in case A above) is made at each point in time to find the vapor and liquid flow rates and properties immediately after the pressure letdown valve (the variables with the primes F , F l, y], x j,.. . shown in Fig. 3.8). These two streams are then fed into the vapor and liquid phases. The equations describing the two phases will be similar to Eqs. (3.40) to (3.42) and (3.44) to (3.46) with the addition of (1) a multi-component vapor-liquid equilibrium equation to calculate Pi and (2) NC — 1 component continuity equations for each phase. Controller equations relating 1 to Fi and P to F complete the model. 

Introduction Binary and Ternary Phase Equilibria 9.2.2.1 Analytical Solutions 92.2.2 General Solutions Calculation Methods for Multi-Component Systems Stepping and Mapping Robustness and Speed of Calculation... 

Clearly CALPHAD has now come of age and is at a watershed where complex phase equilibria calculations can now be performed as a routine operation and yet have also been placed on a sound physical basis. Computer programmes exist which can perform complex calculations on a PC and which can therefore be operated at any location without extensive prior expertise. Furthermore, it is possible in many cases to predict phase equilibria in multi-component alloys to a degree which is close to that expected from experiment (see Chapter 10). It is therefore a branch of science that is mature and, indeed, has already entered the next stage of development, which emphasises the need to concentrate on extending its range of applicability. 

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