A general pressure drop model based on liquid holdup of gas-liquid flow in micro-packed beds

Abstract

The understanding of the gas-liquid flow characteristics in a micro-packed bed reactor is still immature, especially for many gas-organic working systems commonly used in industry. Accordingly, this study proposes a platform to investigate the gas-liquid flow characteristics in a micro-packed bed reactor and presents a unified expression for these characteristics of both organic and aqueous liquid phase. The influence of two-phase flow rate, working solution viscosity, and packing particle size on the liquid holdup and pressure drop were studied. The gas-organic working systems results show that the liquid holdup ranges between 0.5 and 0.8 and pressure drop ranges from 50 to 350 kPa·m−1. In particular, a strong correlation between the two flow characteristics parameters (liquid holdup and pressure drop) was proposed for the first time. Finally, a general pressure drop mathematical prediction model in micro-packed bed were developed.

1. Introduction

Over the past two decades, microreactors have gained considerable attention in the field of chemical engineering due to their remarkable attributions of rapid mixing, exceptional mass transfer capabilities, exceedingly large surface area, and inherent safety [1e4]. As one of the widely developed types of microreactor, the type of micro-packed bed reactors (mPBRs) provides an effective solution to address the low mass transfer efficiency in gas-liquid-solid three-phase reaction systems [5,6]. Due to the large specific surface area of mPBRs with the packing particle less than 500 μm, the use of mPBRs has become an advisable choice in various gas-liquid-solid chemical reaction process intensification, including hydrogenation [7e9] and oxidation [10,11]. Losey et al. [12] first invented mPBRs and reported distinct flow patterns and characteristics compared to large-scale traditional trickle bed reactors (TBRs). The difference of hydrodynamics between mPBRs and TBRs mainly depends on the Bond number (Bo, the ratio of gravitational force to capillary force, Bo = (ρL − ρG)gd_p^2/σ). Because the packing particle size in the mPBR is usually smaller than 500 μm; thus, the Bo number is far less than 1.0, and thereby the gas-liquid microflow in the mPBR is primarily dominated by capillary force and viscous force [13]. As a result, organic solutions and aqueous solutions in micro-channel exhibit very different interfacial phenomena and viscosity characteristics [14]. It is well known that extensive researches on gas-liquid hydrodynamics in TBRs have been reported [15e17]. However, there is a limited amount of literature available on the hydrodynamics (i.e., liquid holdup, pressure drop, residence time distribution, etc.) of micro-packed bed reactors using gas-organic working solution systems. This gap significantly hinders the reliable design of mPBRs for industrial reactions. Therefore, the gas-liquid hydrodynamics in the mPBR is highly required to be studied, especially description of gas-organic system.

For the liquid holdup in mPBRs, van Herk et al. [18] tested the residence time distribution in the mPBR to obtain the liquid holdup, and they found that the flow profiles at the microscale is familiar with the velocity profiles of plug flow, which exhibits a narrow residence time distribution in mPBRs. Márquez et al. [19] measured the liquid holdup in the mPBR and found that the liquid holdup ranges from 0.65 to 0.85, which is significantly higher than the range of 0.05e0.25 in TBRs. The higher liquid holdup in the mPBR signifies the non-ideality of the gas-liquid flow, which leads to the liquid holdup being one of the important flow parameters in the mPBR. Based on a mathematic model proposed by Atton et al. [20] for the large-scale trickle beds, Zhang et al. [21] chosen the water-air working system to derive the predictive formula for the liquid holdup in the mPBR, which contains the two-phase capillary number (Ca). Furthermore, Wang et al. [22] used the glycerol-water and air as the working system and promoted the predictive model for the liquid holdup. However, based on the above-described works, it is evident that investigations on liquid holdup primarily focus on air-water systems, with studies on gas-organic working systems being rare.