Sizing Up Filters

By Dr. Scott Rudge

Of all the unit operations used in pharmaceutical manufacture, filtration is used the most frequently, by far. Filters are used on the air and the water that makes its way into the production suite. They are used on the buffers and chemical solutions that are used to feed the process. They are used to vent the tanks and reactors that the products are held and synthesized in. But the sizing of the filters is largely an afterthought in process design.

Liquid filters that will be used to remove an appreciable amount of solid must be sized with the aid of experimental data. Typically, a depth filter is used, or a filter that contains a filtration aid, such as diatomaceous earth. A depth filter is a filter in which there are no defined pores, rather, they are usually some kind of spun fiber, like polyethylene, that serves as a matt for capturing particulate. You probably did a depth filtration experiment in high school with glass wool. Or you’ve used a depth filter in your home aquarium with the gravel (under gravel filter) or an external filter pump (where the fibrous cartridge you install is a depth filter, such as the "blue bonded filter pads" shown below).

A depth filter uses both its fiber mesh to trap particles, but also then uses the bed of particles to capture more particles. It is actually the nature of the particles that controls most of the filtration properties of the process.

Because of the solids being deposited onto the filter, the resistance of the filter to flow increases as the volume that has been filtered increases. Therefore, knowing the exact size of filter that will be required for your application can be complicated. The complication is overcome by developing a specific solids resistance that is normalized to the volume that has been filtered, and the solids load in the slurry. Once this is done, these depth filters can be sized by measuring the volume filtered at constant pressure in a laboratory setting. The linearized equation for filtration volume is:

By measuring the volume filtered with time at constant pressure, the two filtration resistances can be found as the slope and intercept of a plot of t/(V/A) vs. (V/A). The area of a depth filter is the cross section of the flow path. On scale up, the depth of a depth filter is held constant, and this cross section is increased. An example of the laboratory data that should be taken, and the resulting plots, is shown below:

As expected, the filter starts to clog as more filtrate is filtered. The linearized plot gives a positive y-axis intercept and a positive slope, which can be used to calculate the resistance of the filter and the resistance of the solids cake on the filter.

The resistance of the filter should be a constant and independent of any changes in the feed stream. However, the specific cake resistance, α, will vary with the solids load. It is important to know the solids load in the representative sample(s) tested, and the variability in the solids load in manufacturing. The filter then should be sized for the highest load anticipated. This will result in the under-utilization of the filter area for most of the batches manufactured, but will reduce or eliminate the possibility that the filter will have to be changed mid-batch.

Of course, reducing variability in the feed stream will increase the efficiency of the filter utilization, and reduce waste in other ways, such as reducing variability in manufacturing time, reducing manufacturing investigations and defining labor costs.