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

Includes bibliographical references.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

Numerical simulation of bubble columns by integration of bubble cell model into the population balance framework

Includes bibliographical references.Bubble column reactors are widely used in the chemicals industry including pharmaceuticals, waste water treatment, flotation etc. The reason for their wide application can be attributed to the excellent rates of heat and mass transfer that are achieved between the dispersed and continuous phases in such reactors. Although these types of contactors possess the properties that make them attractive for many applications, there still remain significant challenges pertaining to their design, scale-up and optimization. These challenges are due to the hydrodynamics being complex to simulate. In most cases the current models fail to capture the dynamic features of a multiphase flow. In addition, since most of the developed models are empirical, and thus beyond the operating conditions in which they were developed, their accuracy can no longer be retained. As a result there is a necessity to develop eneric models which can predict hydrodynamics, heat and mass transfer over a wide range of operating conditions. With regard to simulating these systems, Computational Fluid Dynamics (CFD) has been used in various studies to predict mass and heat transfer characteristics, velocity gradients etc (Martín et al., 2009; Guha et al., 2008; Olmos et al., 2001; Sanyal et al., 1999; Sokolichin et al., 1997).The efficient means for solving CFD are needed to allow for investigation of more complex systems. In addition, most models report constant bubble particle size which is a limitation as this can only be applicable in the homogenous flow regime where there is no complex interaction between the continuous and dispersed phase (Krishna et al., 2000; Sokolichin & Eigenberger., 1994). The efficient means for solving CFD intimated above is addressed in the current study by using Bubble Cell Model (BCM). BCM is an algebraic model that predicts velocity, concentration and thermal gradients in the vicinity of a single bubble and is a computationally efficient approach The objective of this study is to integrate the BCM into the Population Balance Model (PBM) framework and thus predict overall mass transfer rate, overall intrinsic heat transfer coefficient, bubble size distribution and overall gas hold-up. The experimental determination of heat transfer coefficient is normally a difficult task, and in the current study the mass transfer results were used to predict heat transfer coefficient by applying the analogy that exists between heat and mass transfer. In applying the analogy, the need to determine the heat transfer coefficient experimentally or numerically was obviated. The findings indicate that at the BCM Renumbers (Max Re= 270), there is less bubble-bubble and eddy-bubble interactions and thus there is no difference between the inlet and final size distributions. However upon increasing Re number to higher values, there is a pronounced difference between the inlet and final size distributions and therefore it is important to extend BCM to higher Re numbers. The integration of BCM into the PBM framework was validated against experimental correlations reported in the literature. In the model validation, the predicted parameters showed a close agreement to the correlations with overall gas hold-up having an error of ±0.6 %, interfacial area ±3.36 % and heat transfer coefficient ±15.4 %. A speed test was also performed to evaluate whether the current model is quicker as compared to other models. Using MATLAB 2011, it took 15.82 seconds for the current model to predict the parameters of interest by integration of BCM into the PBM framework. When using the same grid points in CFD to get the converged numerical solutions for the prediction of mass transfer coefficient, the computational time was found to be 1.46 minutes. It is now possible to predict the intrinsic mass transfer coefficient using this method and the added advantage is that it allows for the decoupling of mass transfer mechanisms, thus allowing for more detailed designs.The decoupling of mass transfer mechanisms in this context refers to the separate determination of the intrinsic mass transfer coefficient and interfacial area

Integrating Rate Based Models into a Multi-Objective Process Design & Optimisation Framework using Surrogate Models

In the development of energy and chemical processes, the process engineers extensively apply computer aided methods to design & optimise these processes and corresponding process units. Such applications are multi-scale modelling and multi-objective optimisation methods. Multi-objective optimisation of super-structured process designs are expensive in CPU-time due to the high number of potential configurations and operation conditions to be calculated. Thus single process units are generally represented by simple models like equilibrium based (chemical or phase equilibrium) or specific short cut models. In the development of new processes, kinetic effects or mass transport limitations in certain process units may play an important role, especially in multiphase chemical reactors. Therefore, it is desirable to represent such process units by experimentally derived rate based models (i.e. reaction rates and mass transport rates) in the process flowsheet simulators used for the extensive multi-objective optimisation. This increases the trust engineers have in the results and allows enriching the process simulations with newest experimental findings. As most rate based models are iteratively solved, a direct incorporation would cause higher CPU-time that penalises the use of multi-objective optimisation. A global surrogate model (SUMO) of a rate based model was successfully generated to allow its incorporation into a process design & optimisation tool which makes use of an evolutionary multi-objective optimisation. The methodology was applied to a fluidised bed methanation reactor in the process chain from wood to Synthetic Natural Gas (SNG). Two types of surrogate model, an ordinary Kriging interpolation and an artificial neural network, were generated and compared to its underlying rate based model and the chemical equilibrium model. The analysis showed that kinetic limitations have significant influence on the result already for standard bulk gas chemical components. A case study applying the previous version of the process design model and the revised version (with rate based model introduced as a set of five surrogate models) will demonstrate that the prediction uncertainties of the process design & optimisation methodology are reduced due to the integration of the rate based model of the fluidised bed methanation reactor. It will be shown that the different process design models predict considerably different optimal operating conditions of the Wood-to-SNG process. This emphasises the importance of the integration of rate based models into the process design models. The presented approach has been developed for the fluidised bed methanation reactor, however, it is a generic approach which can be applied to other process unit technologies as well. Future investigations will target other technologies to further improve the process design & optimisation predictions and support project development