Mixed Up?

By Dr. Scott Rudge

Determining and defending mixing time is a common nuisance in process validation. There are rarely data existing from process development, and there is rarely time or enthusiasm for actually studying the tank dynamics to set mixing times appropriately. Although there typically are design criteria for tank and impeller dimensions, motor size and power input into the tank, these design criteria are rarely translated to process development and process validation functionaries.

http://www.chemineer.com/mixing_technology.php

There are resources for mixing time determination if the basic initial work has been done. A very elegant study is included in the recent PQLI A-Mab Case Study produced by the ISPE Biotech Working Group. This study shows how to scale mixing from a lab scale 50 L vessel where a correlation between power and Reynolds number has been developed, to mixing vessels of 500 and 1500 L scales. The study requires that two critical dimensional ratios remain nearly constant on scale up, the diameter of the impeller divided by the diameter of the tank, and the height of the fluid level to the diameter of the tank. The study shows very close agreement between predicted mixing time and actual mixing time. The basis for the scale up is that the power input per unit mixing volume should be constant from scale to scale.

When the dimensional ratios cannot be kept constant, there are still rules for scale up. For example, as shown in the chart below (from Perry and Chilton’s Chemical Engineers’ Handbook, 5th edition, 1973), as the impeller diameter increases relative to the tank diameter, the relative power requirement declines, but the torque required to turn the impeller increases. This correlation can be used to adjust the power requirement to the scale up condition.

Additionally, there is “general agreement that the effect of mixer power level on mass-transfer coefficient is greater before than after off-bottom motion of all particles in a solute-solvent suspension is achieved (op.cit.)”.

In other words, once particles have been fluidized off the bottom of the vessel, whether they are carried all the way to the top of the vessel or not is not so important when it comes to predicting complete dissolution of the solids. At that point, the mass transfer coefficient is related only weakly to the power input, as shown below. Mass transfer coefficients for the dissolution of solids can be easily determined in the lab, and do not have to be determined again and again for new processes.

Knowing the minimum power requirements for particle suspension and the mass transfer coefficients for the solids being dissolved allows estimation of mixing times required for preparing a buffer. Knowing the mixing time allows the manufacturer to schedule buffer or medium preparation more precisely, eliminating over-processing or incorrect processing (a principle of lean manufacturing) and helps to guarantee a quality reagent/intermediate is produced each time, on time, and ready to implement in the next manufacturing step.

Quality by Design: Dissolution Time

By Dr. Scott Rudge

In a previous post, I discussed the prevalence of statistics used in Quality by Design. These statistical tools are certainly useful and can provide (within their limits of error) prediction of future effects of excursions from control ranges for operating parameters, specifically for Critical Quality Attributes (CQA’s). The limitations of this approach were discussed in the previous blog. In the next series of blogs on Quality by Design, I will discuss opportunities for increasing quality, consistency and compliance for biotechnology products by building quality from the ground up.
While active pharmaceutical ingredient (API) manufacture by biosynthesis is a complicated and difficult to control prospect, there are a number of fundamental operations that are imminently controllable. Media and buffers must be compounded, sometimes adjusted or supplemented, stored and ultimately used in reactors and separators to produce and purify the API. These solutions are fairly easy to make with precision. Three factors come immediately to mind that can be known in a fashion that is scale independent and rigorous, 1) the dissolution rate, 2) the mixing power required and 3) the chemical stability of the solution.

The dissolution rate is a matter of mass transfer from a saturated solution at the dissolving solid interface to the bulk solution concentration. If particle size is fairly consistent, then the dissolution rate is represented by this equation:

where k is the mass transfer coefficient, provided the dissolving solid is fully suspended. It is easy to measure this mass transfer rate in the laboratory with an appropriate measure of solution concentration. For example, for the dissolution of sodium chloride, conductivity can be used. We conducted such experiments in our lab across a range of volumes salt concentrations, and found a scale independent mass transfer coefficient of approximately 0.4 s^-1. An example of the results is shown in the accompanying figure.

With the mass transfer coefficient in hand, the mixing time can be precisely specified, and an appropriately short additional engineering safety factor added. If the times are known for dissolution, and mixing is scaled appropriately (as will be shown in future blogs) then buffers and other solutions can be made with high precision and little wasted labor or material. In addition, the properties of the solutions should be constant within a narrow range, and the reproducibility of more complicated unit operations such as reactors and separators, much improved.

A design based on engineering standards such as this produces predictable results.  Predictable results are the basis of process validation.  As the boiling point of water drives the design of the WFI still, we should let engineering design equations drive Quality by Design for process unit operations.

Leah Choi contributed to this work