When we apply thermodynamics to industrial and research problems, we should draw fundamental ideas from Parts I and II, devise an appropriate solution strategy, as in Chapter 10, and combine those with a computational technique, as in Chapter 11. Such a procedure 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).

PHASE EQUILIBRIA

When two or more bulk phases are in contact and at equilibrium, the measurables of interest are usually temperature, pressure, and the compositions of the phases. Of these measurables, the most important are often the compositions; for example, in the design and operation of separation processes, we routinely need the composition of a particular phase, or when the temperature and pressure change, we need to know the extent to which the compositions also change. When engineering applications involve fluid-fluid equilibria, we often find that, besides absolute compositions, relative compositions can be informative and important.

In the previous chapter we accomplished our first objective: we showed how the process variables heat and work are related to changes in system properties, the internal energy U and the entropy S. Those relations are provided by the first and second laws. Now our problem is to learn how to compute changes in U and S. Since U and S cannot be obtained directly from experiment, we must first relate ΔU and ΔS to measurable state functions, particularly temperature, pressure, volume, composition, and heat capacities. When we can establish such relations, our strategy in a process analysis can take the path on the left branch of the diagram shown in Figure 3.1.

Unfortunately, ΔU and ΔS are not always simply related to measurables, nor are ΔU and ΔS always directly related to convenient changes of state. So to ease conceptual and computational difficulties, we create additional state functions. Then we must establish how ΔU and ΔS are related to these new state functions and, in turn, how changes in the new functions are related to measurables. In these situations, our strategy follows the right branch of the diagram in Figure 3.1. In this chapter we develop relations that allow us to follow both strategies represented in the figure.

Our long-term goal is to be able to analyze processes, and since processes cause changes in system states, we begin by discussing the conditions that must be satisfied to characterize a state (§ 3.1).

When two or more homogeneous systems are brought into contact to form a single heterogeneous system, any of several actions may occur before equilibrium is reestablished. The possibilities include mass and energy transfers, chemical reactions, and the appearance or disappearance of phases. In this chapter we provide thermodynamic criteria for determining whether and to what extent such phenomena actually occur. Surprisingly, these criteria invoke no new thermodynamics—we need only combine familiar thermodynamic quantities in new ways and, in some cases, apply to those quantities mathematical operations that we have not used heretofore.

The heterogeneities of most concern to us are those that involve the presence of more than one phase. The analysis of multiphase systems can be important to the design and operation of many industrial processes, especially those in which multiple phases influence chemical reactions, heat transfer, or mixing. For example, phase-equilibrium calculations form the bases for many separation processes, including stagewise operations, such as distillation, solvent extraction, crystallization, and supercritical extraction, and rate-limited operations, such as membrane separations.

Analysis of multiphase systems is a principal theme of chemistry and chemical engineering; another is analysis of chemical reactions—processes in which chemical bonds are rearranged among species. Rearranging chemical bonds is the most efficient way to store and release energy, it drives many natural processes, and it is used industrially to make substitutes for, and concentrated forms of, natural products.

You are a member of a group assigned to experimentally determine the behavior of certain mixtures that are to be used in a new process. Your first task is to make a 1000-ml mixture that is roughly equimolar in isopropanol and water; then you will determine the exact composition to within ±0.002 mole fraction. Your equipment consists of a 1000-ml volumetric flask, assorted pipettes and graduated cylinders, a thermometer, a barometer, a library, and a brain. You measure 300 ml of water and stir it into 700 ml of alcohol—Oops!—the meniscus falls below the 1000-ml line. Must have been careless. You repeat the procedure: same result. Something doesn't seem right.

At the daily meeting it quickly becomes clear that other members of the group are also perplexed. For example, Leia reports that she's getting peculiar results with the isopropanol-methyl(ethyl)ketone mixtures: her volumes are greater than the sum of the pure component volumes. Meanwhile, Luke has been measuring the freezing points of water in ethylene glycol and he claims that the freezing point of the 50% mixture is well below the freezing points of both pure water and pure glycol. Then Han interrupts to say that 50:50 mixtures of benzene and hexafluorobenzene freeze at temperatures higher than either pure component.

During the design and operation of chemical processes, we routinely propose a state for a system by specifying a temperature, pressure, composition, and phase. Then the question is, Can the system be brought to that state? This is a question of observability. In many situations, particularly those involving multicomponent mixtures, the answer is not at all obvious. For example, at certain values for T and P, mixtures of phenol and water can undergo drastic phase changes in response to slight changes in composition: a mixture of phenol in water might be a one-phase vapor, or a one-phase water-rich liquid, or a phenol-rich liquid in equilibrium with a water-rich liquid, or it might be in three-phase vapor-liquid-liquid equilibrium.

In the previous chapter we derived criteria for identifying equilibrium states; for example, in a closed system at fixed T and P, the equilibrium state is the one that minimizes the Gibbs energy. That minimization is equivalent to satisfying the equality of component fugacities. More generally, we derived criteria for thermal, mechanical, and diffusional equilibrium in open systems. But although those criteria can be used to identify equilibrium states, they are not always sufficient to answer the question of observability. Observability requires stability. Thermodynamic states can be stable, metastable, or unstable; a stable equilibrium state is always observable, a metastable state may sometimes be observed, and an unstable state is never observed.

Introduction

This chapter is the central one of the book; all previous chapters being introductory ones to it, and all posterior chapters arising from this one. Distillation process in infinite column at finite reflux is the most similar to the real process in finite columns. The difference in results of finite and infinite column distillation can be made as small as one wants by increasing the number of plates. Therefore, the main practical questions of distillation unit creation are those of separation flowsheet synthesis and of optimal design parameters determination (i.e., the questions of conceptual design) that can be solved only on the basis of theory of distillation in infinite columns at finite reflux.

The significance of such theory and, in particular, the significance of development of minimum reflux number calculation methods has been clear for numerous investigators all over the world since the beginning of distillation science development. A great number of publications have been devoted to these questions. However, the general distillation theory at finite reflux was created only lately on the basis of unification of several important ideas and theories of geometric nature. One can refer to the latter the idea of examination of distillation trajectory bundles at finite reflux for fixed product composition, the conception of sharp separation of multicomponent mixtures, the theory of location of reversible distillation trajectories in the concentration simplex, the theory of trajectory tear-off from the boundary elements of concentration simplex at finite reflux, and the theory of section trajectories joining.

Introduction

Although the thermodynamically reversible process of distillation is unrealizable, it is of great practical interest for the following reasons: (1) it shows in which direction real processes should be developed in order to achieve the greatest economy, and (2) the analysis of this mode is the important stage in the creation of a general theory of multicomponent azeotropic mixtures distillation.

First investigations of thermodynamically reversible process concerned binary distillation of ideal mixtures (Hausen, 1932; Benedict, 1947). Later works concerned multicomponent ideal mixtures (Grunberg, 1960; Scofield, 1960; Petlyuk & Platonov, 1964; Petlyuk, Platonov, & Girsanov, 1964).

The analysis of the thermodynamically reversible process of distillation for multicomponent azeotropic mixtures was made considerably later. Restrictions at sharp reversible distillation were revealed (Petlyuk, 1978), and trajectory bundles at sharp and nonsharp reversible distillation of three-component azeotropic mixtures were investigated (Petlyuk, Serafimov, Avet'yan, & Vinogradova, 1981a, 1981b).

Restrictions at nonsharp reversible distillation of three-component azeotropic mixtures were studied by Poellmann and Blass (1994).

Trajectories of adiabatic distillation at finite reflux for given product points should be located in concentration space in the region limited by trajectories at infinite reflux and by trajectories of reversible distillation (Petlyuk, 1979; Petlyuk & Serafimov, 1983).

The algorithm, based on this principle and checking for three-component mixtures whether it is possible to get either products of given composition at distillation, was developed by Wahnschafft et al. (1992).

Introduction

This chapter extends the geometric description of the distillation process to infinite complex columns and complexes, and then on this basis to develop methods of their calculation.

Here we understand by complex columns a countercurrent cascade without branching of flows, without recycles and bypasses, which, in contrast to simple columns, contains more than two sections. The complex column is a column with several inputs and/or outputs of flows. The column of extractive distillation with two inputs of flows – feed input and entrainer input – is an example of a complex column.

We understand by distillation complex a countercurrent cascade with branching of flows, with recycles or bypasses of flows. Columns with side stripping or side rectifier and columns with completely connected thermal flows (the so-called “Petlyuk columns”) are examples of distillation complexes with branching of flows. A column of extractive distillation, together with a column of entrainer regeneration, make an example of a complex with recycle of flows. Columns of this complex work independently of each other; therefore, we do not examine it in this chapter, and the questions of its usage in separation of azeotropic mixtures and questions of determination of entrainer optimal flow rate are discussed in the following chapters.

The fundamental difference between complex columns and complexes and simple columns lies in the availability of intermediate sections (besides the top and the bottom ones). The intermediate sections exchange vapor and liquid flows with other sections or with the decanter.

Introduction

Our main purpose is to understand which column sequences can be used in order to get the necessary products. This task is called the task of sequencing (synthesis). The sequencing task is being solved in consecutive order beginning with the first distillation column, where initial n-component mixture comes to. For each column, it is necessary to determine feasible splits.

As a rule, our task is to separate this mixture in a few distillation columns into pure components (perhaps, with the addition of subsidiary components – entrainers, or using, besides distillation, other methods of separation). That is why we are first interested in the sharp splits in each column, when each product of the column contains a number of components smaller than the feeding of the column. The finite number of sharp splits makes determining the sharp splits quite clear and definite.

The important advantage of mixture separability analysis for each sharp split consists of the fact that this analysis, as is shown in this and three later chapters, can be realized with the help of simple formalistic rules without calculation of distillation. A split is feasible if in the concentration space there is trajectory of distillation satisfying the distillation equations for each stage and if this trajectory connects product points. That is why to deduct conditions (rules) of separability it is necessary to study regularities of distillation trajectories location in concentration space.