(153a) A Novel Approach to the Experimental Determination of Njs Using Electrical Resistance Tomography

N_js, the minimum agitation speed needed to just suspend all the solid particles in a solid-liquid mixture stirred in an agitated vessel, is a critical parameter to properly operate industrial mixing tanks and reactors in a large number of industrial operations. As a result, a significant literature on N_js is available. The oldest and most common method to measure N_js experimentally is that of Zwietering’s (Chem. Eng. Sci., 1958, 8, 244-253), where N_js can be visually obtained by determining the agitation speed at which the solids remain at the bottom of the tank for no more than 1-2 seconds before being swept away. Although this has been shown to be a reliable method to obtain N_js, it still relies on visual observation of the bottom of the vessel and it is therefore potentially susceptible to observer’s bias. To address this issue new observed-independent experimental approaches to determine N_js using measurements of the fraction of solids on the vessel bottom were previously developed by our research group. However even those methods are unsuitable to be used in opaque fluids/tanks or if images of the vessel bottom cannot be taken.

In order to experimentally determine N_js even in systems where the tank content cannot be inspected, a novel method using Electrical Resistance Tomography (ERT) was developed and tested in this work. Accordingly, a sensor array probe consisting of a straight plastic rod mounting 16 electrodes was placed vertically in a fully baffled mixing tank provided with a centrally mounted agitation system and containing water and non-conductive glass beads approximately 300 µm in diameter. The electrodes were connected to an external ERT system and data acquisition apparatus (P2+ System, Industrial Tomography Systems, Manchester, UK) dynamically measuring the conductivity distribution and resistivity in the solid-liquid system data between each pair of adjacent electrodes. The apparatus consisted of a signal source, voltmeters, electrode multiplexer array, signal demodulators, and a system controller, connected to a computer. The system generated Alternating Current (AC) between pairs of neighboring electrodes and the resulting voltage was measured across all other neighboring electrodes. Current injection was applied to all neighboring electrodes. Through this approach it was possible to measure the mean bulk resistance across the electrodes on the sensing array probe, measure the conductivity distribution on a portion of a vertical place inside the tank, and also obtain 2-D images of the conductivity distribution inside the tank through the use of image reconstruction algorithms.

In a typical experiment the array probe was placed in the tank, and after proper calibration, the mean bulk resistance of the solid-liquid mixture was obtained as the mixture was stirred by an impeller in the mixing tank at different values of the impeller agitation speed, N. As N increased, increasingly larger fractions of the non-conducting solids became suspended, thus increasing the resistivity of the suspension measured by the ERT apparatus. A plot of the percent resistance variation vs. the agitation speed resulted in an S-shaped curve, which eventually reached an asymptotic limit value as all solids became suspended and dispersed in the liquid. In order to extract N_js from the data, a mathematical approach previously developed by our groups for a different system was used (Huang and Armenante, Chem. Eng. Sci., 1992, 47, 2865-2870). Accordingly, the experimental data were interpolated with cubic spine curves and the agitation speed at which the function F(N), equal to the ratio of the second derivative to the first derivative of the combined spine curve function, showed a minimum point was takes as the N_js value (N_js-ERT). The rationale for this approach is as follows: F(N) represents how the change in slope of the spline curve (second derivative) with respect to the spline curve slope (first derivative) varies with N. F(N) can be expected to reach a minimum value when the spline function is just about to bend to approach the asymptote.

Experiments were conducted where N_js-ERT was obtained under different operating conditions, i.e., where the impeller type, impeller ratio-to-tank diameter ratio, and impeller clearance were varied. N_js was not only experimentally obtained using the proposed ERT approach but also using the Zwietering method as well as the method recently developed by Shastry and Armenante (AIChE Meeting, Minneapolis, 2017). Then, parity plots were constructed in which N_js-ERT was plotted against the N_js values obtained with the other two methods. Excellent agreement was observed in all plots, indicating that the novel method proposed here can be effectively used for the experimental determination of N_js.

The results of this work show that ERT combined with the analysis of the data proposed here can be used to effectively measure N_js in solid-liquid dispersion in mechanically stirred vessels. The proposed approach is observer-independent and can be used even in systems that cannot be directly observed, such as industrial tanks. Therefore, it is expected that this approach could find extensive practical applications in the chemical, pharmaceutical and biopharmaceutical industries.