Intensifying micromixing in a semi-batch reactor using a Rushton turbine

Abstract

The ‘iodide–iodate’ reaction scheme has been used to ascertain the effectiveness of micromixing in a semi-batch reactor when feeding with pipes rotating and discharging continuously into the region of highest local specific energy dissipation rate, ${\epsilon }_T$. The results are compared with those obtained using a fixed pipe at the equivalent position and at other positions including near the top surface, the most convenient position industrially. The results show significant intensification, i.e., a seven-fold reduction in ‘waste product’, between the most convenient fixed feed pipe position and the rotating pipes, even at the modest specific power input of $\sim 1.0\mathrm{W}/\mathrm{kg}$. This mode of addition also ensures that feeding is always into a constant value of ${\epsilon }_T$, whereas with a static pipe close to the impeller the reactants are being fed in a region where ${\epsilon }_T$ varies cyclically. This difference in the ${\epsilon }_T$ values experienced by the two modes of addition poses problems for previous models of micromixing in the literature linking selectivity to local specific energy dissipation rates.

Introduction

Mixing at the molecular scale (micromixing) is important in processes such as polymerization, precipitation and in determining the selectivity of competing fast chemical reactions. Therefore, a lot of work in the last few years has been done on micromixing, developing experimental methods (Baldyga and Bourne, 1999, David et al., 1985, Fournier et al., 1996) to characterize it. During this time, experimental techniques like laser Doppler velocimetry and particle image velocimetry (PIV) have significantly improved, giving more reliable values of ${\epsilon }_T$, the local specific energy dissipation rate. Knowledge of the values of this parameter is important as high levels enhance micromixing.

Rushton turbines (RTs) have been extensively studied and the flow patterns and the turbulence properties, including the spatial distribution of ${\epsilon }_T$, for this impeller are relatively well known. Nienow and Wisdom (1974) and Van’t Riet and Smith (1975) both reported the presence of a trailing vortex pair behind each blade where very high rotational shear rates were found and the latter tried to identify the position of their axis using flow followers combined with a photographic technique. Since then, many other authors (Lee and Yianneskis, 1998, Sharp and Adrian, 2001, Stoots and Calabrese, 1995, Yianneskis and Whitelaw, 1993, Yianneskis et al., 1987, for example) have studied the flow structure close to the RT with laser based methods giving a more precise indication of the position of the vortex axis (Fig. 1) and the value of other turbulence parameters. Takahashi and Nienow (1992) used the vortex cavity structure produced at very low gas flow rates to show the vortex axis position and found similar results. Lee and Yianneskis (1998) found that the maximum values of turbulent kinetic energy in the vessel are present in the vortex at a position $15–{30}^{\circ }$ behind the Rushton blades.

Estimation of the value of ${\epsilon }_T$ for RTs has been made by a number of authors. Cutter (1966) was the first to use a tracer/photographic technique and latterly laser-based techniques have been used, e.g., Zhou and Kresta (1996) and Schäfer (2001). All concluded that most of the energy was dissipated in the impeller discharge stream. For example, Wu and Patterson (1989) found that 60% of the energy transmitted to the tank from the impeller was dissipated in the impeller and the impeller discharge stream. Other authors have tried to measure the maximum local ${\epsilon }_T$ value; for example, Cutter (1966) based on his streak photography whilst Wu and Patterson (1989) and Schäfer (2001) and many of the others listed above used a laser-based technique. Overall, agreement between different workers has been poor and values of $({\epsilon }_T{)}_{\max }/{\overline{\epsilon }}_T={\phi }_{\max }$ from $\sim 20$ to $\sim 140$ have been reported by Zhou and Kresta (1996) as the impeller, $D$, to tank diameter, $T$, ratio was reduced from $\frac{1}{2}$ to $\frac{1}{4}$. This range of ${\phi }_{\max }$ encompasses the values found by all the workers. This variation in the values reported in the literature arises not only from the different $D/T$ ratios utilised but also from the assumptions and numerical manipulations required to obtain ${\epsilon }_T$ from the raw, randomly fluctuating velocity data. It is also necessary to consider the complexity associated with the presence of a regular fluctuating component due to the blade passage and whether ${360}^{\circ }$ ensemble data or angle resolved data should be used. In addition, close to the impeller, all parameters vary very significantly, even for very small changes in position.

Predictions of ${\epsilon }_T$ values have also been made by computational fluid dynamics. Typically $k–\epsilon$ models have been used. Again, these studies show the highest values in the impeller discharge stream. More recently, estimates of ${\phi }_{\max }$ have been made for the trailing vortex using the sliding mesh technique, e.g. Ng and Yianneskis (2000) giving ${\phi }_{\max }\cong 40$ and Bujalski (2003) giving a ${\phi }_{\max }\cong 25$. However, it should also be recognised that generally, when local ${\epsilon }_T$ values based on the $k–\epsilon$ model have been integrated over the volume of the tank to give ${\overline{\epsilon }}_T$, very low values of ${\overline{\epsilon }}_T$ compared to the experimental ones have been found (Bujalski, 2003).

In our previous paper (Assirelli et al., 2002), we used the ideas summarized above to pick a precise fixed feed point for optimizing micromixing in a semi-batch reactor. Thus, the feed was introduced through a fixed pipe positioned at 1.04 times the radius of the RT and at the top of the blade, estimated from the literature to be the location of ${\phi }_{\max }$. The consecutive feeding, iodide–iodate technique (Guichardon and Falk, 2000) was used to assess the effectiveness of this feed position for the optimization of micromixing. It was found that this position minimized the amount of unwanted material compared to that produced at three other fixed positions further away from the impeller. For example, for a particular set of conditions, it could be reduced from $\sim 20\%$ when feeding near the top of the vessel to $\sim 5\%$ (Assirelli et al., 2002). A similar result confirming the effectiveness of this feed position for a semi-batch reactor was found by Schäfer (2001). He also estimated ${\phi }_{\max }\cong 50$ in good agreement with the value that he obtained by LDA.

Given this result, it was decided to see if even more efficient micromixing could be achieved by feeding into the region of highest ${\epsilon }_T$ continuously. In other words, in the previous work, though the feed was continuous, it was only intermittently into this region, depending at any instant on the position of the feed pipe relative to the precise position of a single impeller blade. Thus, only six times per revolution of the impeller would the feed be into the region of maximum ${\epsilon }_T$ and then only briefly. However, if the feed point rotated with the impeller, feed could be maintained 100% of the time into the point of maximum ${\epsilon }_T$. This paper reports the results from developing such a feed method.