Issue link: https://www.e-digitaleditions.com/i/1000772
Tablets & Capsules July 2018 31 The mean centered variance (MCV) is the variance (square of the standard deviation) normalized by the square of the mean value of the distribution. In this case, the mean value of the distribution is the mean residence Figure 5 Blender RTD profiles at 350 and 400 rpm 7.00 6.00 5.00 4.00 3.00 2.00 1.00 0.00 -1.00 Tracer concentration (percentage by mass) Time (minutes) Start at 350 rpm Increase to 400 rpm (21:57) Tracer added (27:33) Tracer added (3:53) 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 Figure 4 a. Tracer properties similar to material properties Effect of tracer properties on RTD profile b. Tracer bulk density much higher than material bulk density 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00 18 16 14 12 10 8 6 4 2 0 -2 Tracer concentration (percentage by mass) Tracer concentration (percentage by mass) Time (minutes) Time (minutes) 0.00 5.00 10.00 15.00 0.00 10.00 20.00 30.00 Measuring a blender's residence time distribution D e t e r m i n i n g a b l e n d e r ' s R T D i s c r i t i c a l t o understanding and characterizing the blender's operation. The RTD helps you understand how material flows through the blender as well as how effectively the blender will filter incoming noise from the unit operation immediately upstream. Determining the blender's RTD also enables you to develop feed-forward (downstream) and feed-back (upstream) control strategies to ensure the final product's quality. If you have incoming noise from a feeder or unit operation directly upstream, you can use the blender's RTD to predict the composition of the blender's output stream. You can then take feed-forward action to either reject out-of-spec product or take corrective action in downstream unit operations to bring the product back within specifications. You can also take feed-back action to eliminate the source of the noise. A blender's RTD can be measured by introducing an instantaneous pulse of a tracer material into the material stream and measuring the tracer concentration at the blender's outlet as a function of time, as shown in Figure 3. As the figure shows, the sharp pulse at the feeder inlet is broadened at the outlet due to axial convection as the tracer moves through the blender. The RTD function [E(t)] is defined by the equation: Where t is time and c(t) is the tracer concentration as a function of time. The mean residence time (τ) is defined by the equation: Lastly, the mean centered variance (σ 2 ) is defined by the equation: ∫ º ∞ c(t).dt c(t) E(t) = ∫ º ∞ τ = t.E(t).dt ∫ º ∞ σ 2 = (t-τ) 2 .E (t).dt τ 2 τ τ Tracer added Tracer added