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The quadrature method of moments (QMOM) is a recent technique of solving population balance equations for particle dynamics simulation. In this paper, an alternative solution for the QMOM is described and thoroughly tested, which is based on the formulation and simultaneous solution of a semi-explicit differential algebraic equation (DAE) system. The DAE system consists of the ordinary differential equations resulting from the application of the method of moments, as well as a system of nonlinear algebraic equations derived by applying the quadrature theory for the approximation of the moments. It is shown that the proposed approach provides an efficient procedure for evolving the quadrature abscissas and weights from the QMOM. The Jacobian matrix of the DAE system is provided analytically to make the solution more robust. The DAE-QMOM method is compared to the well-established method for solving QMOM based on the product difference (PD) algorithm. The numerical results are compared to the analytical solutions in the case of breakage, aggregation, growth, and nucleation mechanisms. Excellent agreements are found on the moment evolution predicted by both methods. However, the DAE-QMOM method is found to be more accurate and robust than the PD-QMOM in some cases. Additionally, the DAE-QMOM is also capable of providing the solution significantly faster than the PD-QMOM method.

Abstract.A combined computational fluid dynamics (CFD) and population balance model (PBM) approach has been applied to the simulation of gas-liquid stirred tanks agitated by (i) a Rushton turbine or (ii) a CD-6 impeller, operating at aeration numbers from 0.017 to 0.038. The multiphase simulations were realised via an Eulerian-Eulerian two-fluid model and the drag coefficient of spherical and distorted bubbles was modelled using the Ishii-Zuber equations. The effect of the void fraction on the drag coefficient was modelled using the correlation by Behzadi et al. (2004). The local bubble size distribution was obtained by solving the PBM using the quadrature method of moments (QMOM). The local k L a was estimated using both the Higbie penetration theory and the surface renewal model. The predicted gas-liquid hydrodynamics, local bubble sizes and dissolved oxygen concentration were in good agreement with experimental measurements reported in the literature. A slight improvement in the prediction of the aerated power number was obtained using the non-uniform bubble size distribution resulting from the coupled CFD-PBM simulation. Evaluation of the prospective scale-up approaches indicates a higher probability of maintaining a similar level of mass transfer in a larger tanks by keeping the P g /V and VVM constant. Considering its predictive capability, the method outlined in this work can provide a useful scale-up evaluation of gas-liquid stirred tanks.

This work presents a computational fluid dynamics (CFD) calculation to predict and to evaluate the effects of temperature and inlet velocity on the pressure drop of gas cyclones. The numerical solutions were carried out using spreadsheet and commercial CFD code Fluent 6.1. This paper also reviews four empirical models for the prediction of cyclone pressure drop, namely [Air pollution control: a design approach, in: C. David Cooper, F.C. Alley (Eds.), Cyclones, second ed., Woveland Press Inc., Illinois, 1939, p. 127-139] [Chem. Eng. (1983) 99] [Doctoral Thesis, Havarad University, USA, 1988], and [Chem. Eng. Progress (1993) 51]. All the predictions proved to be satisfactory when compared with the presented experimental data. The CFD simulations predict excellently the cyclone pressure drop under different temperature and inlet velocity with a maximum deviation of 3% from the experimental data. Specifically, results obtained from the computer modelling exercise have demonstrated that CFD is a best method of modelling the cyclones operating pressure drop.

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This work presents a computational fluid dynamics (CFD) calculation to predict and to evaluate the effects of temperature and inlet velocity on the pressure drop of gas cyclones. The numerical solutions were carried out using spreadsheet and commercial CFD code Fluent 6.1. This paper also reviews four empirical models for the prediction of cyclone pressure drop, namely [Air pollution control: a design approach, in: C. David Cooper, F.C. Alley (Eds.), Cyclones, second ed., Woveland Press Inc., Illinois, 1939, p. 127-139] [Chem. Eng. (1983) 99] [Doctoral Thesis, Havarad University, USA, 1988], and [Chem. Eng. Progress (1993) 51]. All the predictions proved to be satisfactory when compared with the presented experimental data. The CFD simulations predict excellently the cyclone pressure drop under different temperature and inlet velocity with a maximum deviation of 3% from the experimental data. Specifically, results obtained from the computer modelling exercise have demonstrated that CFD is a best method of modelling the cyclones operating pressure drop.

A 3 wt% La-promoted Ni/Al2O3 catalyst was prepared via wet co-impregnation technique and physicochemically-characterized. Lanthanum was responsible for better metal dispersion; hence higher BET specific surface area (96.0 m2 g−1) as compared to the unpromoted Ni/Al2O3 catalyst (85.0 m2 g−1). In addition, the La-promoted catalyst possessed finer crystallite size (9.1 nm) whilst the unpromoted catalyst measured 12.8 nm. Subsequently, glycerol dry reforming was performed at atmospheric pressure and temperatures ranging from 923 to 1123 K employing CO2-to-glycerol ratio from zero to five. Significantly, the reaction results have yielded syngas as main gaseous products with H2:CO ratios always below than 2.0 with concomitant maximum 96% glycerol conversion obtained at the CO2-toglycerol ratio of 1.67. In addition, the glycerol consumption rate can be adequately captured using power law modelling with the order of reactions equal 0.72 and 0.14 with respect to glycerol and CO2 whilst the activation energy was 35.0 kJ mol−1. A 72 h longevity run moreover revealed that the catalyst gave a stable catalytic performance.

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