A fundamental approach to predicting mass transfer coefficients in bubble column reactors

A bubble column reactor is a vertical cylindrical vessel used for gas-liquid reactions. Bubble Columns have several applications in industry due to certain obvious advantages such as high gas-liquid interfacial area, high heat and mass transfer rates, low maintenance requirements and operating costs. On the other hand, attempts at modelling and simulation are complicated by lack of understanding of hydrodynamics and mass transfer characteristics. This complicates design scale-up and industrial usage. Many studies and models have attempted to evolve understanding of the hydrodynamic complexity in Bubble Columns reactors. A closer look at these studies and models reveals a variety of solution methods for different systems (Frössling, 1938; Clift et al., 1978; Hughmark, 1967; Dutta, 2007; Ranz and Marshall, 1952; Benitez, 2009; Buwa et al., 2006; Suzzia et al., 2009; Wylock et al., 2011). Numerous correlations (Frössling, 1938; Clift et al., 1978; Hughmark, 1967; Dutta, 2007; Ranz and Marshall, 1952; Benitez, 2009; Buwa et al., 2006) exist but to date in literature, there is no general approach to determining accurate estimates of average mass transfer coefficient values. Good estimates of the average mass transfer coefficient will improve the predictive capacity of the associated models. Recent attempts at modelling micro-scale bubble-fluid interaction resulted in the Bubble Cell Model, BCM, (Coetzee et al., 2009) which simulates the velocity vector field around a single gas bubble in a flowing fluid stream using a Semi-Analytical model. The aim of the present study is to extend the BCM applications by integrating the mass balance into the framework to predict the average mass transfer coefficient in bubble columns. A nitrogen-water steady state system was simulated in an axisymmetric grid where mass transfer occurs between the gas and liquid. iv A concentration gradient may develop around the bubble which may be represented as concentration contours, where the mass boundary layer thickness as defined in the film theory is identified as one of these contours. The width of the irregularly shaped mass boundary layer thickness may be averaged and together with the nitrogen mass diffusivity used to calculate the average mass transfer coefficient. The local fluid velocity affects the thickness of the film and together with the nitrogen mass diffusivity influences the rate of mass transfer across the concentration boundary layer. Increasing the inlet velocity decreases the mass boundary layer thickness and thereby increases the average mass transfer coefficient. The CFD results from the simulation were integrated into the BCM by developing an algebraic function using the curve fitting approach. Three different ways of estimating mass transfer coefficient were developed, namely, the Sherwood number, concentration boundary layer (film theory) and boundary layer models. The best and fastest model with R value of 0.9956 was the film theory now called the BCM Extension, which estimates the mass transfer coefficient as a function of Re and Sc numbers. The BCM extension results were compared to different correlations such as those of Frössling (1938), Clift et al. (1978), Ranz and Marshall (1952); the estimated results showed not only the expected trend but also similar values to the mass transfer coefficient. The close estimates show there is a relation between the simulation model and correlations from experiments. Therefore, a two dimensional semi-analytical fundamental model, the BCM, can be used to generate the steady-state velocity vector and pressure fields and when given the Reynolds and Schmidt numbers, predict the gas-liquid mass transfer rate from spherical bubbles in bubble columns in a homogeneous regime.