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

Development of a computationally efficient monolith reactor simulator: CFD-hybrid model analysis of methane oxidation monolith catalysed systems.

Doctoral Degrees. University of KwaZulu-Natal, Durban.The optimisation of complex geometries such as that of monolith reactors can be supported by computation and simulation. However, complex boundaries such as those found in multi-channel monoliths render such simulations of extremely high computational expense. Adding to the computational expense is the strong coupling among reaction kinetics, heat and mass transfer limitations in these channels. This severely limits the possibilities for geometric optimisation. In the first step toward developing a fast-solving hybrid simulation, a detailed CFD simulation was used to obtain the unsteady state, spatial temperature and concentration (and hence reaction rate) profiles for a range of input conditions. The results of the CFD simulation were then accepted as the benchmark to which faster-solving models were measured against to be considered as viable descriptions. A modified plug flow with effectiveness factor correction for wall mass-transfer was developed and evaluated as the first step towards the development of a multi-channel model. However, the modified plug model is only applicable to single channel monoliths and cannot account for heat transfer across high-density multi-channel beds. For multichannel simulations, the modified plug flow model is embedded into a hybrid-model framework. The hybrid model is based on the principle that, due to the high density of channels in a monolith, there will exist an equivalent homogeneous cylindrical model that approximates the behaviour of a bundle of channels acting as axial heat sources. This model entails the coupling of analytical solutions to single channel mass and momentum transfer with heat transfer across the single-shell extra-multi-channel space. Due to the application of effectiveness-factor type approaches, it is shown that the model can be represented by algebraic models that accurately represent the partial differential equations (PDEs) that describe monolith reactors. A close agreement between both temperature and species mole fraction profiles predicted from the modified plug flow model and a detailed CFD model was found with R2 values of 0.994 for temperature. The time needed to find a converged solution for plug flow model on an Intel(R) Core(TM) i5-5300U CPU @ 2.30GHz workstation was found to be 53 seconds in comparison to 1.3 hours taken by a CFD model. The hybrid model was itself validated against the CFD multichannel model. The hybrid model axial temperature and species concentration profiles at various radial positions were found to be in a close agreement with CFD simulations, with relative error found to be in the 0.35 % range. The clock time on an Intel(R) Core(TM) i5-5300U CPU @ 2.30GHz workstation was found to be 38 hours for a CFD multi-channel simulation which when compared with the 53 seconds clock time of the hybrid model implies the suitability of hybridisation for the application to geometric optimisation in the design of monolith reactors. The hybrid-model is developed to facilitate geometric optimization with the view of reducing hot spot formation, pressure drop and manufacturing costs. This is because monolith reactors applied in catalytic partial oxidation of methane are coated with precious metal catalysts, significantly contributing to capital costs. By isolating regions of high catalytic activity, it becomes possible to reduce the amount of precious metal coating required to achieve high conversion. The fast-solving hybrid model was used in the economic analysis of the catalytic partial oxidation of methane to syngas. Due to the low computational expense of the hybrid model, it was possible to investigate a wide range of design geometry and operating condition .It is shown that, for methane oxidation over a Platinum gauze catalyst, the channel diameter could be optimised to the 0.8 mm level resulting in the highest syngas revenue (R 65754.14 /day). The distribution of the catalytic material on the monolithic walls was found to influence the reactor performance hence the process profitability. The non-uniform distribution was found to significantly reduce the cost of fabrication while maintaining a high syngas productivity. In general, a method is proposed to optimise design and operation of catalytic monolith reactors through the application of fast-solving models.Author's Keywords : Hybrid model, catalytic partial oxidation, modified plug flow model, CF

CFD Modelling of Gas-Solid Reactions: Analysis of Iron and Manganese Oxides Reduction with Hydrogen

Metallurgical processes are characterized by a complex interplay of heat and mass transfer, momentum transfer, and reaction kinetics, and these interactions play a crucial role in reactor performance. Integrating chemistry and transport results in stiff and non-linear equations and longer time and length scales, which ultimately leads to a high computational expense. The current study employs the OpenFOAM solver based on a fictitious domain method to analyze gas-solid reactions in a porous medium using hydrogen as a reducing agent. The reduction of oxides with hydrogen involves the hierarchical phenomena that influence the reaction rates at various temporal and spatial scales; thus, multi-scale models are needed to bridge the length scale from micro-scale to macro-scale accurately. As a first step towards developing such capabilities, the current study analyses OpenFOAM reacting flow methods in cases related to hydrogen reduction of iron and manganese oxides. Since reduction of the oxides of interest with hydrogen requires significant modifications to the current industrial processes, this model can aid in the design and optimization. The model was verified against experimental data and the dynamic features of the porous medium observed as the reaction progresses is well captured by the model