Computational strategies, equilibrium phase

COMPUTATIONAL STRATEGIES FOR MAPPING EQUILIBRIUM PHASE DIAGRAMS 3... 

The phenomenon of phase behavior is the organization of many-body systems into forms which reflect the interplay between constraints imposed macro-scopically (through the prevailing external conditions) and microscopically (through the interactions between the elementary constituents). In this article we focus on generic computational strategies needed to address the problems of phase behavior, or more specifically the task of mapping equilibrium phase boundaries. 

In addition to its generality, the form (7.1.48) is important because it leads to a computational strategy for analyzing phase-equilibrium situations. In that strategy, a phase-equilibrium problem is treated as a multivariable optimization in which the Ihs of (7.1.48) is the quantity to be minimized. An alternative strategy, in which the computational problem is to solve a set of coupled nonlinear algebraic equations, arises from the constraints on open-system processes developed in 7.2. 

We now do for reaction-equilibrium problems what we have done in 10.1 for phase-equilibrium problems we show how fundamental thermodynamic relations are used to develop computational strategies. We start by discussing the number of independent properties required to identify states in reacting systems ( 10.3.1) then we... 

In a similar way, phase equilibrium problems can be solved with the Gibbs energy minimization technique. Some computational strategies are presented in [71-... 

The strategy of design, illustrated in Figure 8.1, consists of an evolutionary search of the feasible design space by means of a systematic combination of thermodynamic analysis, computer simulation and only limited experiments. The approach is generic for developing a RD process, at least for similar systems. The first element of similarity is the existence of an equilibrium reaction with water as product This raises the problem of possible aqueous-phase segregation. The second element is the similarity of thermodynamics properties over a class of substrates. However, while the fatty acids and fatty esters manifest a certain... 

We will need values of conceptuals for two classes of problems (a) calculation of thermodynamic properties for one-phase systems and (b) calculation of multiphase and chemical reaction equilibria. For both kinds of problems, we use the same basic strategy (i) Compare raw or modeled experimental data with computed properties of an ideal substance to obtain measures for deviations from the ideality, then (ii) exploit the deviation measures to obtain expressions for the required conceptuals in terms of measurables. Calculations of one-phase properties are typically based on differences, while phase and reaction equilibrium calculations typically use ratios. In 6.2.1 and... 

Figure 6.2 Schematic illustration of the strategies used to obtain computational forms for fugacities, which are needed for phase- and reaction-equilibrium calculations. Traditionally, route 2A has been mostly used for gases, while route 2B was confined to condensed phases. However, these uses were dictated, not by thermodynamic limitations, but by limitations of the models used to correlate the data.

When we apply thermodynamics to industrial and research problems, we should draw fundamental ideas from Parts 1 and 11, devise an appropriate solution strategy, as in Chapter 10, and combine those with a computational technique, as in Chapter 11. Such a procedme provides values for measurables that can be used to interpret novel phenomena, to design new processes, and to improve existing processes. The procedure is illustrated in this chapter for several well-developed situations. They include conventional phase-equilibrium calculations for vapor-liquid, liquid-liquid, and solid-solid equilibria ( 12.1) solubility calculations for gases in liquids, solids in liquids, and solutes in near-critical solvents ( 12.2) independent variables in steady-flow processes ( 12.3) heat effects for flash separators, absorbers, and chemical rectors ( 12.4) and effects of changes of state on selected properties ( 12.5). 

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