(174j) Scale-up of Stirred Tanks Applied to Newtonian Liquids

The processes of agitation and mixing of liquids in tanks with mechanical impellers are widely applied at chemical, petrochemical, food and pharmaceutical industries. Tanks are such versatiles equipments, since they can be designed as chemical reactors, heat exchangers, distiller tank, extraction tank, dilution tank, decanters, floating tank and storage tanks.

The design of a new stirring unit includes the determination of the mechanical impeller power consumption; mixing time; and when applied to heat exchangers processes, also includes the determination of the required thermal exchange area. However, the forementioned variants also depends of the type of the tank (cylindrical or square), type of impeller (axial or radial), baffles, fluids physical properties and rheology behavior, which increases the complexity of the design calculation during the project.

Since the unprecedented paper published by Rushton, Costich e Everett (1950) regarding the determination of standard dimensions for stirred tanks based on the lowest power consumption and the best mixing quality, until current researches as the one published by Rosseburg et. al. (2018), that looks into the interconnection between high volumes tanks (in order of 15 m³) and the mixing time; there are countless expressions for design project calculation; power consumption, mixing time and overall heat transfer coefficient.

Even though, most part of those equations have had their parameters fundamented by empirical experimentation at laboratory scale units or semi-pilots units, so that the used tanks have small diameters, meanwhile industrial units use to have bigger diameters. During design calculation steps, the most important question must be: which rotation should be applied to the industrial tank so that the observed phenomena at the smaller scale tank prevails at the same way and efficiency at the larger tank?

The scale up is the technique that should answer this question in an effective way. In 1976, Hicks, Morton e Fenic, have developed a scale up method based on a mixing scale (that variates from 1 to 10) and at the mechanical impeller pumping capacity, which turns this technique into an exclusive method only for axial impellers. Anyhow a mixing scale must be assumed that will not always represent the real phenomena, which may end up in an oversizing motor, wasting much energy.

Penny (1971) has established a method based on the scale enlargement between tanks by geometric similarity, where the impeller rotation at the larger tank is obtained from coupling parameters, such as: a) equal tip-speed, b) equal Reynolds number, c) equal overall heat transfer coefficient, d) equal Froude number, e) equal mixing time and f) equal power-volume unit ratio. To make this technique a trustful one, it is mandatory that the experiments be conducted at least into three tank with different diameters.

Even though, many authors used to publish expressions for scale up based on Penny´s method, though their experimentation being conducted in only two tanks, which may cause imprecision at extrapolation step for larger units.

Based on literary deficiency, the authors of the current paper have had as goal, the proposal of expressions for scale up at Newtonian liquids mixing process using three tanks with different volumes and two types of impellers (axial and radial).

The experiments were conducted at three mixing units composed by 1.0 hp; 2.2 hp e 15.0 hp motors coupled to two types of impellers, the axial model with 4 blades 45º and the radial model 6 flat blades bolted to disk support, at flat bottom tank with internal diameter (D_T) of 0.23m (V_net 10L); 0.40m (V_net 50L) e 0.98m (V_net 740L). All units have been designed according to Rushton, Costich e Everett (1950) standards, so that the impeller diameter, D_a=D_T/3; impeller height from the flat bottom, E=D_a; fluid level, H=D_T; the four baffles width, J=D_T/10; impeller blades width, W= D_a/5 and impeller blades length, L=D_a/4. In each unit two Newtonian fluids were applied: water and 20% sucrose solution (in weight).

All tests were conducted in batch process under steady temperature of 25ºC. The desired outputs (speed rotation and power consumption) were pointelly measured with portable instrumentation device (tachometer and dynamometer), being shifted in 10 levels and submitted to repetitive procedure for each set of configuration: tank, impeller and fluid.

The mathematical models for scale up prediction were obtained by nonlinear multiple regression between the power – volume unit ratio (P/V), Reynolds number (Re) and tank internal diameter (D_T) for each impeller, by the combination of a pair called D_Tj (higher volume tank) and D_Ti (lower volume tank).

Thus, two models composed by 600 observed points each, were developed following the general function: [(P/V)_j/(P/V)_i]=(N_j/N_i)^a(D_Tj/D_Ti)^2a+b at a confidence interval of 95%. The axial impeller provided a model with adjusted determination coefficient (R²_adj) of 0.951 and determination coefficient (R²) of 0.953. The radial impeller originated a model with adjusted determination coefficient (R²_adj) of 0.972 and determination coefficient (R²) of 0.974.

For the axial impeller, the expoent “a” were obtained as 2.324 and the expoent “b” as 3.376. Besides that, for the radial impeller, the expoent “a” were obtained as 2.548 and the expoent “b” as -3.931.

Depending on the project scope, the general model can be applied under different approaches, according to which parameter is desired to be constant, por example at the same impeller tip-speed the equation can be remodeled as [(P/V)_j/(P/V)_i]=(N_i/N_j)^(a+b). Even the same Reynolds number can be requested, [(P/V)_j/(P/V)_i]= (D_Tj/D_Ti)^b or the same power – volume unit ratio, (N_i/N_j)^-a=(D_Tj/D_Ti)^2a+b.

The empirical models were crosschecked by experimental validation for a scale up scenario of 74:1, with three different rotations. The axial impeller demonstrated a standard deviation of 29% whereas the radial impeller indicated a standard deviation of 14%

The models proposed by Penny (1971) were compared under the same conditions, so that the deviation measured for the axial 4 blades 45º was in a range of 15-28%. However the same model could not be applied to the radial model impeller with 6 flat blades bolted to disk support, since the deviation achieved values around 66-142%.

The axial impeller has a more organized flow pattern, so that the deviation between the models with 2 tanks from Penny (1971) and 3 tanks (current research) have exhibited a reasonable deviation. Even though the radial impeller, which generates high turbulence, presented a high deviation from the 2 tanks prediction model, that indicates that it is necessary an additional tank to rectify potential mathematics non-linearity at equations models, since that the 3 tanks model deviation was 14%

Lastly, the 3 tanks model presented at the current study are applicable to a Reynolds range of 12,551 – 665,057 for the axial impeller and 12,676 – 620,720 for the radial impeller; scale up of 74:1, besides a power – volume unit ratio range of 0.050 – 3.905 for the axial impeller and 0.069 – 12.00 for the radial impeller.