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Beta ratio

Until recently there has not been any universally accepted test method to measure or describe the media pore size or the size of particles a filter media can capture and hold. Fortunately now a test procedure called multi-pass testing or Beta ratio testing is a universally accepted test method that yields readily comparable test results.
It was introduced with the object of giving both filter manufacturer and user an accurate and representative comparison amongst filter media.

Multi-pass testing uses a specified contaminate, of known sizes, added regularly in measured quantities to the fluid which is pumped continuously through the filter. Measured samples of the fluid are then taken at timed intervals from both the downstream and the upstream of the filter simultaneously, particles are measured and counted by electronic means using automatic particles counters.
From these measurements a Beta ratio (b) is formulated by dividing the number of particles of a particular size in the upstream flow by the number of particles of the same size in the downstream flow:

where b_x is the beta ratio for contaminant larger than x mm
N_u is the number of particles larger than x mm per unit of volume upstream
N_d is the number of particles larger than x mm per unit of volume downstream.

The beta ratio is an indicator of how well a filter controls particulate: i.e., if one out of every two particles (>xmm) in the fluid pass through the filter, the beta ratio at xmm is 2, if one out of every 200 of the particles (>xmm) pass through the filter the beta ratio is 200.
Therefore, filters with a higher beta ratio retain more particles and have higher efficiency.
Efficiency for a given particle size (E_x) can be derived directly from the beta ratio by the following equation:

The following table lists some selected beta ratios and the correspondent efficiency:

b value to x mm	Cumulate efficiency %
bx	for particles x mm
1.00	0.00
1.50	33.00
2.00	50.00
10.00	90.00
20.00	95.00
50.00	98.00
75.00	98.70
100.00	99.00
200.00	99.50
1000.00	99.90
10000.00	99.99

Source: 'Filters and Filtration Handbook', T Christopher Dickenson, Elsevier, January 1, 1997

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