Gas flow maldistribution in random packed beds of non-spherical particles – A CFD study

Highlights

• Gas maldistribution in random packed bed studied with particle resolved direct numerical simulation.

• Packing of rings distribute the flow similarly to full cylinders but with much smaller pressure drop.

• At the outlet from packing of full cylinders strong localised jets are formed.

• Flow maldistribution is the smallest when the gas inlet is tangential to the wall of the distribution chamber.

Abstract

In this work, gas maldistribution in random packings of cylinders and Raschig rings is studied with particle-resolved direct numerical simulation (PRDNS) employing a finite volume solver for Cartesian grids and the immersed boundary method for the treatment of complex geometries. The geometry of the random packed bed has been obtained in a separate simulation based on a sequential deposition of particles in a cylindrical column and a simplified mechanics with additional radial force allowing for higher packing densities. The first part of the work focuses on comparison of the packings of cylinders and rings with respect to their ability to distribute the flow uniformly over the cross-section of the column when the gas in the form of a narrow jet enters along the column axis and impinges on the bed directly. The second part is devoted to analysis of three different inlet configurations and their influence on gas maldistribution in the packing of Raschig rings. It has been found that the random packing of rings has comparable properties of flow uniformisation to the same arrangement of full cylinders with significantly lower pressure drop and much less pronounced effect of formation of localised jets at the bed outlet. Among the considered inlet configurations the most beneficial is the one in which the gas duct is tangential to the walls of the distribution chamber.

Introduction

In many areas of chemical engineering packed beds are often employed as one of the most important component of the system. They can take a form of a regular structure (structured packing) or a random packing of particles filling a cylindrical column and can be encountered in equipment like absorbers, desorbers, distillation towers or trickle bed reactors (Billet, 1995, Maćkowiak, 2010). For reacting components (liquid or gaseous) introduced into the system, the packed bed provides a very large contact surface area improving the efficiency of the chemical reaction or heat and mass transfer. From the point of view of such applications uniform distribution of reactants within the bed is crucial for ensuring full utilisation of the bed surface, preventing so-called hot spots in highly exothermic reactions or other undesired effects. However, as observed by many researchers and practitioners, uniform distribution at the inlet to the packing column does not have to be maintained when the fluids travel through the complex structure of the bed. This is particularly true for liquids and liquid maldistribution has been extensively studied both experimentally (Fourati et al., 2012) and numerically (Du et al., 2015). The liquid reactant tends to gather on the walls of the column (wall flow effect) or forms rivulets covering only specific parts of the bed leaving other parts unwetted (channeling effect), see Kolev (2006).

Studies concerning gas maldistribution are much scarcer, as it is generally believed that properly distributed at the inlet, gas flow remains uniform within the packing (Olujic et al., 1991). In fact, it has been shown that gas radial spreading is much more significant than that of liquid (Kouri and Sohlo, 1996, Stikkelman et al., 1989). For beds of large height to diameter ratio, gas maldistribution in comparison to liquid maldistribution can be disregarded but for shallow beds, with diameter larger than their height, non-uniformity of the gas flow may be pivotal to the performance of the system (Porter et al., 1993). Shallow beds are not so rarely used in practice – petroleum rectification columns, cooling towers or equipment in which low pressure drop is required. The major problem occurs when the gas is introduced into a column through a small diameter duct (relative to the column diameter) and enters the distribution chamber in the form of a high-velocity jet that can persist up to some distance in the packing (penetration length $l_{\mathit{pen}}$; see Green and Perry, 2007, Edwards et al., 1999). Thus, proper design of gas distributors is of significant importance but, surprisingly, this subject has not been widely studied – see Muir and Briens (1986) as an example of experimental work in this area and Haghshenasfard et al. (2007) as a numerical one.

There are some works analysing gas maldistribution in other systems like fluidised (Patel et al., 2008) or moving beds (Paterson et al., 2000).

Most of the previous studies concentrate on uniformisation of flows in structured packings (see Stikkelman et al., 1989, Darakchiev, 2010, Olujic et al., 1991, Olujic, 2011) and random packed beds are treated only in a few works (see Porter et al., 1993 or Kouri and Sohlo, 1996 where both liquid and gas distribution are considered). In these works, maldistribution is assessed by measuring flow velocity near the bed outlet where a probe can be placed easily. The evolution of flow within the bed can be reconstructed by building the bed layer by layer like in Olujic (2011) or with non-intrusive but expensive tomographic techniques (Fourati et al., 2012). In the case of liquid maldistribution, the spreading of liquid can be examined to a certain extent with an optical method (Niegodajew et al., 2018).

Numerical models seem to be one of the most promising tools for analysis of flows in complex structures, including random packed beds. By its nature, a numerical simulation gives full information about the flow characteristics beyond the reach of any known experimental technique but extensive validations are required before a particular computational model gains trust at the same level as physical measurements. In the literature, numerous works treat the packed bed as a homogeneous medium with effective properties and averaged flow equations are solved with additional terms taking into account the influence of the particles on the macro-scale flow characteristics. This approach is preferred when a detailed, direct, micro-scale simulation cannot account for relevant complex phenomena (e.g. chemical reaction, capillarity, liquid-to-surface adhesion, turbulence) or required grid resolution would be prohibitive at the considered scale – see Bazmi et al., 2012, Iliuta et al., 2012, Yang et al., 2013, Niegodajew and Asendrych, 2016, Asendrych and Niegodajew, 2017. However, flow simulations in a real geometry of the packing become more and more popular in last 15 years – see Nijemeisland et al., 2004, Guardo et al., 2005, Augier et al., 2010, Robbins et al., 2012, Owens et al., 2013, Marek, 2017, Dong et al., 2017 or the recent review article of Jurtz et al. (2018). Studies of this type typically concern single-phase flows and focus on calculation of pressure drop. Some of them even take into account chemical reactions and heat transfer but virtually all use uniform inlet conditions.

The purpose of the present work is to apply the numerical model, developed by the author and described in Marek (2017), to analysis of gas flow maldistribution in random packed beds of non-spherical particles – here cylinders and Raschig rings. In contrast to other studies, like Edwards et al. (1999) or Parsons and Porter (1992), the Navier-Stokes flow equations are solved in a real geometry of the packing without any additional model terms. The advantage of the proposed flow model is that it does not require the generation of a computational grid fitted to the particles. Typically, generation of such grids is troublesome and original geometry of the bed needs to be slightly modified (see Dixon et al., 2013, Sosnowski et al., 2018).

The first part of the study is devoted to comparison of two types of packing particles, the second focuses on influence of various inlet configurations.