To simulate the expected bubble-point value of various multiround setups the automated integrity test bubble-point test algorithm
was programmed in an Excel (Microsoft) spreadsheet, and the diffusion profiles of the individual cartridges were entered.
The authors found that it should be possible to get a clear bubble-point test failure involving the 10-in. bubble-point failing
cartridge in a multiround setup (cartridges A, B, C, D, F, and G). In addition, the authors found that it should not be possible
to get a bubble-point test failure when including the failing 10-in. high-diffusion cartridge in a multiround set-up (cartridges
A, B, C, D, F, and H), because no exponential increase would be expected to take place before the minimum bubble point.
Multipoint diffusion limit curve
The diffusion profile of a filter cartridge can be plotted in two distinct areas, with the applied differential pressure on
the x-axis and the resulting diffusion on the y-axis.The first area is the so called diffusive flow region, where the diffusion rate can be considered linear as a function
of the applied test pressure. In this test-pressure region, the pores are still filled with the wetting liquid.
The second region is the so-called bulk flow region where the applied pressure gradually blows out an increasing number of
pores, giving a free-gas flow through the membrane. The flow graph turns exponential.
Figure 4: Small filter surface inflection point versus large filter surface inflection point. (ALL FIGURES ARE COURTESY OF
THE AUTHORS.)
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Between the linear and exponential area is the so-called inflection point or transition phase. The sharpness of the inflection
point is directly related to pore-size distribution, pore design, and the size of the filter surface. The smaller the filter
surface and the more homogeneous the pore-size distribution, the sharper the inflection point (see Figure 4).
Figure 5: Multipoint diffusion test limit curve. (ALL FIGURES ARE COURTESY OF THE AUTHORS.)
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The multipoint diffusion limit curve is based on the diffusive flow and the bulk flow and is defined by three set points.
It is a straight line from the first test pressure point, which is the common single-point diffusion-test pressure (in this
case 2500 mbar or 36.25 psi), up to a point at 100 mbar before the minimum bubble point (in this case 3100 mbar or 44.95 psi).
The last point at 50 mbar after the minimum bubble point (in this case 3250 mbar or 47.15 psi). This much higher maximum allowable
diffusion rate allows one cartridge to reach the bubble point at the minimum bubble point without giving a false failed test
result (see Figure 5).
The maximum allowable diffusion value for the two first pressure steps is calculated taking into account the number of cartridges,
their individual maximum allowable diffusion value, the applied test pressure, and a safety margin. The maximum allowable
diffusion value for the last test-pressure point is calculated taking into account the same variables as the two previous
set points but allowing one cartridge to reach bubble point. This is achieved by adding a cartridge size-related diffusion
value representing the over-proportional increase generated by the bulk flow at the bubble point. In the integrity-test unit
bubble point test algorithm, this value is called the A2-value (c.f. Functional Design Specification of Sartocheck 3, Sartocheck 3+, Sartocheck 4). The set point equations thus
become:
First set point at p1:
Diffmaxp1 = nbDiffmaxindividual@p1
α
Second set point at p2:
Diffmaxp2 = nbDiffmaxindividual@p1
α(p2/p1)
Third set point at p3:
Diffmaxp3
= (nb – 1)Diffmaxindividual@p1
α(p3/p1) + A2
in which nb is the number of cartridges in the multiround housing, nb – 1 is the value of nb minus the cartridge eventually reaching the bubble point, Diffmaxindividual@p1 is the validated maximum allowable diffusion value for the concerned cartridge type (here 54 mL/min), α = (1 – safety margin),
p1 is the standard diffusion test pressure (here 2500 mbar or 36.25 psi), p2 is the second set point (here 3100 mbar or 44.95 psi), p3 is the third and last set point (here 3250 mbar or 47.15 psi), and A2 is the cartridge size–related diffusion value (here 240 mL/min).
During out-of-box trials using new 30-in. Sartopore 2 filter cartridges, the typical diffusion value was only slightly higher
than half of the maximum allowable diffusion value given by the manufacturer. During the simulation trials, a maximum allowable
diffusive flow limit one-third lower than the standard manufacturer's limit created a robust test result without causing false
failures. The a-value was thus set to two-thirds, and the programmed multipoint diffusion limit line became:
Max diffusion at p1 = 5 x 54 x (2/3) = 180 mL/min
Max diffusion at p2
5 x 54 x (2/3) x (3100/2500) = 223.2 mL/min
Max diffusion at p3
(5-1) x 54 x (2/3) x (3250/2500) + 240 = 427.2 mL/min
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