Chemical reactions occur in many commonly practiced separation processes. By chemical reactions, we mean those molecular interactions in which a new species results (Prausnitz et al., 1986). In a few processes, there will be hardly any separation without a chemical reaction (e.g. isotope exchange processes). In some other processes, chemical reactions enhance the extent of separation considerably (e.g. scrubbing of acid gases with alkaline absorbent solutions, solvent extraction with complexing agents). In still others, chemical reactions happen whether intended or unintended; estimation of the extent of separation requires consideration of the reaction. For example, in solvent extraction of organic acids, the extent of acid dissociation in the aqueous phase at a given pH should be taken into account (Treybal, 1963, pp. 38–41). Chemical equilibrium has a secondary role here, yet sometimes it is crucial to separation.

Familiarity with the role of chemical reactions in separation processes will be helpful in many ways. This is especially relevant since a few particular types of chemical reactions occur repeatedly in different separation processes/techniques. These include ionization reactions, acid–base reactions and various types of complexation reactions. The complexation reactions also include the weaker noncovalent low binding energy based bonding/interactions identified in Section 4.1.9. A better understanding and quantitative prediction of separation in a given process is possible, leading to better process and equipment design. In processes where a chemical agent is used, different agents can be evaluated systematically. On occasions, it may facilitate the introduction of reactions to processes for enhancing separation.

In this chapter, we cover those separation processes/techniques where two bulk phases or regions flow through the separation device such that the force(s) driving the separation act perpendicular to the directions of flow of both phases/regions. Section 8.1 describes those separation devices where the two phases or regions have bulk motions countercurrent to each other in the separation device. This section also covers those larger multistage separation devices where the overall pattern of flow vs. force corresponds to countercurrent flow, even through the local flow configurations in a stage may utilize other flow vs. force arrangements for the two flowing phases. Invariably, these separations will be studied under continuous flow of two phases/regions and steady state conditions. The focus will be primarily on phase equilibrium based processes driven by chemical potential gradient such as gas absorption, distillation, solvent extraction, melt crystallization and adsorption. Limited attention has been paid to membrane based processes such as dialysis, electrodialysis, liquid membrane processes, gas permeation and external force driven processes of gas centrifuge (thermal diffusion and mass diffusion are also considered here). Section 8.2 will be concerned with separations where the two phases or regions flow in a cocurrent fashion. Continuous flow of two phases/regions as well as discontinuous flow of one of the phases will be covered. Section 8.3 will focus on those configurations where the two bulk phases are in crossflow in the device. The force(s) will continue to act perpendicular to the flow directions of the two bulk phases in both Sections 8.2 and 8.3.

The basic objective of this chapter is to describe the organization of this book vis-à-vis separations from a chemical engineering perspective. Separation, sometimes identified as concentration, enrichment or purification, is employed widely in large industrial-scale as well as small laboratory-scale processes. Here we refer primarily to physical separation methods. However, chemical reactions, especially reversible ones, can enhance separation and have therefore received significant attention in this book. Further, we have considered not only separation of mixtures of molecules, but also mixtures of particles and macromolecules.

The number of different separation processes, methods and techniques is very large. Further new techniques or variations of older techniques keep appearing in industries, old and new. The potential for the emergence of new techniques is very high. Therefore, the approach taken in this book is focused on understanding the basic concepts of separation. Such an approach is expected not only to help develop a better understanding of common separation processes, but also to lay the foundation for deciphering emerging separation processes/techniques. The level of treatment of an individual separation process is generally elementary. Traditional equilibrium based separation processes have received considerable but not overwhelming attention. Many other emerging processes, as well as established processes dealing with particles and external forces, are not usually taught to chemical engineering students; these are integral parts of this book. To facilitate the analysis of processes over such a broad canvas, a somewhat generalized structure has been provided. This includes a core set of equations of change for species concentration, particle population and particle trajectory. These equations are expected to be quite useful in general; however, separation systems are quite often very complicated, thereby limiting the direct utilization of such equations.

In Section 3.3, we illustrated the thermodynamic relations that govern the conditions of equilibrium distribution of a species between two or more immiscible phases under thermodynamic equilibrium. In Section 4.1, we focus on the value of the separation factor or other separation indices for two or more species present in a variety of two-phase separation systems under thermodynamic equilibrium in a closed vessel. The closed vessels of Figure 1.1.2 are appropriate for such equilibrium separation calculations. There is no bulk or diffusive flow into or out of the system in the closed vessel. The processes achieving such separations are called equilibrium separation processes. Separations based on such phenomena in an open vessel with bulk flow in and out are studied in Chapters 6, 7 and 8. No chemical reactions are considered here; however, partitioning between a bulk fluid phase and an individual molecule/macromolecule or collection of molecules for noncovalent solute binding has been touched upon here. The effects of chemical reactions are treated in Chapter 5. Partitioning of one species between two phases is an important aspect ever present in this section.

The criteria for thermodynamic equilibrium in a single-phase system in a closed vessel subjected to an external force field were also developed in Section 3.3. Based on these criteria, we develop in Section 4.2 estimates of the separation achieved in a single phase in the closed vessel. These estimates are also developed in a closed vessel when an additional property gradient, e.g. density gradient, pH gradient, etc., exists across the vessel length. Focusing is the term often used to characterize the latter separation techniques. In this section, we cover in addition the extent of separation achieved when a temperature gradient is imposed on a single-phase system in a closed vessel not subjected to any external force field.

Separation is a major activity of chemical engineers and chemists. To separate a mixture of two or more substances, various operations called separation processes are utilized. Before we understand how a mixture can be separated using a given separation process, we should be able to describe the amount of separation obtained in any given operation. This chapter and Chapter 2 therefore deal with qualitative and quantitative descriptions of separation. Chapter 2 covers open systems; this chapter describes separations in a closed system.

In Section 1.1, we briefly illustrate the meaning of separation between two regions for a system of two components in a closed vessel. Section 1.2 extends this to a multicomponent system. In Section 1.3, various definitions of compositions and concentrations are given for a two-component system. In Section 1.4, we are concerned with describing the various indices of separation and their interrelationships for a two-region, two-component separation system. A number of such indices are compared with regard to their capacity to describe separation in Section 1.5 for a binary system. Next, Section 1.6 briefly considers the definitions of compositions and indices of separation for the description of separation in a multicomponent system between two regions in a closed vessel. Finally, Section 1.7 briefly describes some terms that are frequently encountered.

We have studied a variety of separation processes and techniques. Our focus was on developing an elementary understanding of an individual separation process/technique. In practice, more often than not, a combination of more than one separation process is employed, regardless of the scale of operation involved. Here we introduce very briefly the separation sequences employed in a few specific industries. The separation sequences of interest are considered under the following headings: bioseparations (Section 11.1); water treatment (Section 11.2); chemical and petrochemical industries (Section 11.3); hydrometallurgical processes (Section 11.4). It is to be noted here that often the separation sequences are reinforced by chemical reactions within such a sequence or before/after the separation steps. The intent here is to provide an elementary view of the complexity and demands of practical systems where certain types of separation sequences are crucial/primary/dominant components.

More often than not, we will find that certain types of separation techniques and processes are much more prevalent in certain industries. For example, solvent extraction and back extraction processes are dominant in the recovery and purification of metals and metallic compounds via hydrometallurgical processes. On the other hand, distillation and, to a much lesser extent, absorption/stripping followed by solvent extraction are the primary separation processes in the chemical/petrochemical industries. Water treatment industries/plants are however, focused much more on deactivation/removal of biological contaminants, suspended materials and dissolved impurities from water via oxidation processes, filtration, membrane techniques and ion exchange processes. Biological separations share some of these characteristics of water treatment processes in terms of the separation techniques; however, since the focus is on recovering/purifying the biologically relevant compound, processes such as chromatography are in great demand.

Scope

This chapter describes the stratified pattern observed in gas–liquid flows, for which liquid flows along the bottom of a conduit and gas flows along the top. The gas exerts a shear stress on the surface of the liquid. It is desired to calculate the average height of the liquid layer and the pressure gradient for given liquid and gas flow rates. The flow is considered to be fully developed so that the height of the liquid is not changing in the flow direction and the pressure gradient is the same in the gas and liquid flows.

In order to consider stratified flow in circular pipes, the simplified model of the flow pattern, presented by Govier & Aziz (1972), is exploited. The interface is pictured to be flat. At large gas velocities, some of the liquid can be entrained in the gas. This pattern is considered in Section 12.5 entitled “the pool model” for horizontal annular flow.

Prologue

Horizontal annular flows differ from vertical annular flows in that gravity causes asymmetric distributions of the liquid in the wall layer and of droplets in the gas flow. The understanding of this behavior is a central problem in describing this system. Because of these asymmetries, entrainment can increase much more strongly with increasing gas velocity than is found for vertical flows.

Theoretical analyses of the influence of gravity on the distribution of liquid in the wall film and on the distribution of droplets in the gas phase are reviewed. As with vertical annular flows, entrainment is considered to be a balance between the rate of atomization of the wall film and rate of deposition of droplets. Because of the asymmetric film distribution, the local rate of atomization varies around the pipe circumference. This is treated theoretically by assuming that the local rate is the same as would be observed for vertical annular flow. Gravitational settling contributes directly to deposition so that the rate of deposition is enhanced. Thus, at low gas velocities, entrainment can be much smaller for horizontal annular flows than for vertical annular flows.

Prologue

Particles entrained in a turbulent fluid are dispersed by velocity fluctuations; they assume a motion that is related to the fluid turbulence. If the suspension flows through a conduit, deposition on a wall depends on the particle turbulence. An understanding of these processes is needed to describe the annular flow regime for which liquid flows along the walls and as drops in the gas flow. The fraction of liquid that is entrained by the gas depends on the rate at which the film is atomized and the rate at which drops deposit on the film.

Equations for trajectories of spherical drops and bubbles in a turbulent flow field are developed. These are used to relate the turbulence properties and the dispersion of particles to the turbulence properties of the fluid in which they are entrained. Of particular interest is the development of relations for the influence of drop size on drop turbulence and on drop dispersion.

Prologue

A central issue to be addressed in analyzing the behavior of bubbles in a gas–liquid flow is understanding the free-fall velocity of a spherical solid particle and the rise velocity of a spherical bubble in an infinite stationary fluid. Analytical solutions for these systems are available for very low particle Reynolds numbers (Stokes law and the Hadamard equation). A derivation of Stokes law is presented in the first part of this chapter.

Experiments show that Stokes law is valid for particle Reynolds numbers less than unity. For larger ReP, empirical correlations of the drag coefficient are used. The description of the rise velocity of bubbles is complicated by possible contamination of the interface. Measurements of the rise velocity of single bubbles are usually presented as plots of US versus the bubble size for a given system. The structure of these plots reflects changes in the shape and behavior of the bubbles. Very large bubbles take the shape of a cap. A prediction of the rise velocity of these cap bubbles, developed by Batchelor, is presented in Section 8.7.

Need for a phenomenological understanding

The one-dimensional analysis and the correlations for frictional pressure drop and void fraction (presented in Chapter 1) have been widely used as a starting point for engineering designs. However, these correlations have the handicap that the structure of the phase boundaries is ignored. As a consequence, they often give results which are only a rough approximation and overlook phenomena which could be of first-order importance in understanding the behavior of a system.

It is now recognized that the central issue in developing a scientific approach to gas–liquid flows is the understanding of how the phases are distributed and of how the behavior of a multiphase system is related to this structure (Hanratty et al., 2003). Of particular interest is the finding that macroscopic behavior is dependent on small-scale interactions. An example of this dependence is that the presence of small amounts of high molecular weight polymers can change an annular flow into a stratified flow by damping interfacial waves (Al-Sarkhi & Hanratty, 2001a).

Prologue

Chapter 2 gives considerable attention to slug flow because of its central role in understanding the configuration of the phases in horizontal and inclined pipes. Several criteria have been identified to define the boundaries of this regime: (1) viscous large-wavelength instability of a stratified flow; (2) Kelvin–Helmholtz instability of a stratified flow; (3) stability of a slug; (4) coalescence of large-amplitude waves. Bontozoglou & Hanratty (1990) suggested that a sub-critical non-linear Kelvin–Helmholtz instability could be an effective mechanism in pipes with very large diameters, but this analysis has not been tested. A consideration of the stability of a slug emerges as being particularly important. It explains the initiation of slugs for very viscous liquids, for high-density gases, for gas velocities where wave coalescence is important and for the evolution of pseudo-slugs into slugs. Chapter 2 (Section 2.2.5) outlines an analysis of slug stability which points out the importance of understanding the rate at which slugs shed liquid. Section 9.2 continues this discussion by developing a relation for Qsh and for the critical height of the liquid layer needed to support a stable slug. Section 9.3 develops a tentative model for horizontal slug flow. Section 9.4 considers the frequency of slugging.

Necessary conditions for the existence of slugs

Figure 9.1 presents simplified sketches of the front and the tail of a slug in a pipeline. The front has a velocity cF; the back has a velocity cB. The stratified liquid layer in front of the slug has a velocity and area designated by uL1, AL1. The mean velocity of the liquid in the slug is uL3. The slug is usually aerated; the mean volume fraction of gas in the slug is designated by α. The gas at station 1 is moving from left to right at a velocity uG1. The assumption is made that the velocity fields can be approximated as being uniform.