I guess the best way to classify safety integrity is by defining Single, Tandem & Double seals.
Single Seals:
In the event of a seal failure, product will leak to atmosphere. If product is hazardous then single seal may not be acceptable.
Tandem Seal Un Pressurized Buffer fluid:
In the event of a Primary seal failure, the Secondary seal will contain the leakage. This assumes Plan 52 Liquid Tandem Seal. It is unlikely for both seals to fail together.
You may consider dry running back up seals but these seals need to be tested with a false air or nitrogen signal to check the seals integrity.
Double Seals Pressurized Barrier Fluid:
This is top of the range. These seals ensure that in the event of a seal failure, Barrier fluid leaks to the process or to atmosphere Plan 53A, B or C. Product cannot leak to atmoshere because the barrier fluid is pressurised above process pressure.
Both Tandem & Double seal systems include instrumentation such as Level & Pressure transmitters to alarm the operator in the event of seal failure or if the system requires top up.
trust this helps