Process Technology: An Introduction - Haan A.B. 2015

17 Hydrodynamic aspects of scale-up
17.1 Introduction

In this chapter an introduction to scale-up in the chemical process industry, and especially in mixing and stirring, is given. In the first part some basic principles of mixing are given, together with an overview of the most common impeller types and mixing operations. In the second part the tools at hand to perform scale modification are discussed, and the last part consists of a short introduction to computational fluid dynamics (CFD). CFD is a relatively new technique, which has become popular with the increase in computing power seen in the last decade.

Scale-up is a very important step in the design of a new plant. Because of the enormous costs involved, it is not possible to perform experiments for process design on full plant scale as the process would be when finally operational. Therefore experiments have to be done on a smaller scale, but these have to be representative for the full-scale process. To make sure the experiments represent the full-scale process, several aspects have to be considered. A simple example of the problems encountered in scale-up is the decrease of surface area relative to the volume of an apparatus, which is for example, important in cooling. If a sphere is considered, the surface area and volume can be calculated by, respectively, 4 · π · r2 and 4/3 · π · r3, and thus their ratio (area/volume) by 3/r. Cooling a large vessel will therefore only be possible by introducing extra coils inside the vessel. The hydrodynamics of a set-up, i.e. the (fluid) flow, can also differ significantly for increased equipment size. This has been the subject to a great deal of research, as it is certainly an influence on product yield and quality. Examples of common hydrodynamic problems in chemical engineering are the occurrence of dead zones, channeling and bypasses in mixing tanks as illustrated by Fig. 17.1.

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Fig. 17.1: Important examples of hydrodynamic problems in scale-up.

To scale up in a structured way and design representative experiments, dimensional, regime, and similarity analysis are very useful (and necessary) tools. Dimensional analysis is the theory in which several dimensionless numbers are used to describe a process. These can be geometrical ratios, ratios of forces in play, and so on. One of the most important numbers is the Reynolds number, named after Osborne Reynolds (1842—1916) who studied fluid flow in pipes, among other phenomena. Because of its importance, the Reynolds number is discussed in this section, and it will be used throughout this chapter to illustrate several principles. It represents the ratio of inertial force and viscous force. In case of fluid flow through a pipe, the Reynolds number Re is given by

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(17.1)

where ρ is the liquid density, v the liquid velocity, d the diameter of the pipe, and η the liquid dynamic viscosity. The Reynolds number is an indication for the flow regime present, in this case, in the pipe. Since the flow regime has a large influence on the rate at which for example heat and mass transfer occur, it can be understood that it is very important to have a representative dimensionless number. If Re < 2000 (low velocity) the flow is laminar (Fig. 17.2a), and if Re > 2000 (high velocity) the flow is turbulent (Fig. 17.2b).

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Fig. 17.2: Velocity profiles for different flow regimes: (a) laminar flow; (b) turbulent flow.

In a laminar flow regime almost no transport of heat or mass takes place in the radial direction. Therefore heat and mass transfer is relatively poor in laminar regimes, and heating or cooling a liquid in a pipe will almost always take place in a turbulent regime.