## Gas diluters and metrology

It’s evident that, due to the type of service (quality test on gas analyzers) gas dividers belong to the metrology world. It’s also evident that gas dividers outlet is not a measurement : they go through two flow measuring, but at the end the output value is just a number (for example, having measured gas to be diluted flow=2L/min. and total output flow = 10L/min., the output value is Dilution ratio=2/10.

The value 2 L/min is not critical : it could be 20 what’s realy importanti is the flows ratio.

It exists at least another “tool” with the same type of performances : the piece counting scale. Also in this case two weigth measurements are done (the reference with one or few peaces and the counting hopper with the peaces to be counted) just for having their ratio.

Two so special devices should receive a special threatment : in the counting tool i’m sure it’s not wrong using as reference some of the peaces of the same family of that to be counted (internal reference violating traceability rule).

But now let’s come back to our diluters : we did setup a procedure that get advantage from the particolar structure of gas dividers series BetaCAP60 to give them a self test function. Reading the following description requires some attention, than you can find the same concepts expressed in a different way in a PowerPoint file following the present link

## Self referring test with BetaCAP60

The construction of BetaCAP60 with two equal capillaries benches, each composed by 5 growing capillaries number equal each other.

Two groups have 1 capillary each, two have 2 capillaries each two have 4, two have 8 and two have 15 capillaries each

As told in the introduction, the dilution ratio quality must be assured, but the flows used to calculate it just require to be each other in a given proportion : multiplying all of them by the same coefficient don’t change the result in terms of dilution ratio. Than, one capillaries group the one with one capillary placed in the upper module will be named “Our reference” and will receive a flow value to that all the other groups must refer.

Test is made by 5 phases uncorrelated one each other : each phase will handle groups containing the same capillaries number with applied the same pressure, that induces very similar flows. The first phase is handling 1 capillary groups, the second 2 capillaries groups, the third 4, the fourth 8 and the fifth 15.

The above flows must be measured : to do that in the diluter it’s istalled an optional meter made by a series of capillaries (to produce a differential pressure when crossed by the flow) and a differential pressure sensor indicating the flow. The flow meter capillaries are activated by 4 solenoid valves selecting 5 measuring sensitivities : The maximum to measure lower flows (through 1 capillary), one half of that to measure phase 2 flows (through 2 capillaries) and so on : the sensitivity is reduced as the flow to be measured increase, in a way of having always nearly the same pressure drop in the sensor and a constant resolution. Scope of this test is to measure/calculate the deviations to the rule that the flows (applying the same pressure) resulting from each capillaries group are proportional to the numerical consistency of the relevant group. In fact this is the consequence if the supposed capillaries equality : if they are equal, dilution is perfect, if not, the deviations can be used to calculate (and correct) the dilution deviation. The equality of the capillaries used in the flow meter is not critical = the two or three measurements made in one phase just request offset null and linearity response. Sensitivity just is request stable. Changing the phase, the sensitivities ratio are not critical : flow measured in one phase cannot be mixed with flow measured in a different phase, because the scale factor is not known. Ratios between measurements made in one phase can be used together with ratios between measurements made in a different phase : each repetition of the 5 phases is preceded by an offset calibration. Relative deviations in fact are herited from one phase to the next .

The comparison that is operated in each phase (after the first) is made between the flows sum through the two groups verified in the previous phase and each of the group with double number capillaries : the flows equality is written, including the flows correction by absolute deviations (some calculated in the previous phase and some not known will be the result of the actual calculation).

## Phase 1

The flows induced in the upper module groups are identified by the name s1, s2, …s15 ; The flows induced in the lower module groups are identified by the name d1, d2, ….d15.

Sensitivities of the different measuring ranges used in each phase are not metrologically related each other, but are in reverse proportion with the flow to be measured : this assure a constant high resolution.

Activating the flow s1, it’s measured the value s1: as already explained, this value will be our reference. All the other values will be evaluated as function of the proportion between the measured value and the capillaries number content in the group. We can then confirm that εr (s1)=0

Activating the flow d1, it’s measured the value d1 and written the formula εr(d1)=(d1-s1)/d1

For next use, we calculate R1= s1/d1

## Phase 2

Activating the flow s2, it’s measured the value s2

Activating the flow d2, it’s measured the value d2

Activating the flows s1 and d1, it’s measured the value sum of the flows s1 and d1

We then write two equations:

s1d1-εr(s1)*(s1′)-εr(d1)*(d1′)=s2-εr(s2)*s2

s1d1-εr(s1)*(s1′)-εr(d1)*(d1′)=d2-εr(d2)*d2

But that’s not correct ! we know that flow measurements cannot be mixed in the same equation if not measured all in one phase (s1’ and d1’are measured in phase 1 and s2, d2, are measured in Phase 2.. Hopefully we have two important information :

R1=s1/d1 that, being a ratio can be used wherever in different phases

and s1d1= s1+d1 measured in phase 2 and then directly available in phase 2. Joining in a system the two equations, s1’=R1*s1d1/(1+R1) and d1’=s1d1/(1+R1) We can then calculate εr(s2) and εr(d2)

For next use, we calculate R2=s2/d2

Passo 2 : si misura a2

Passo 3 : si misura b2

## Phase 3

very similar to phase 2 (the range 4 is activated)

Activating the flow s4, it’s measured the value s4

Activating the flow d4, it’s measured the value d4

Activating the flows s2 and d2, it’s measured the value sum of the flows s2 and d2 (s2d2)

It’s enough to change the indexes of the previous equation from 1 to 2 and from 2 to 4 to calculate εr(s4) e εr(d4)

## Fase 4

Once activated, the s8 flow is measured

Once activated, the flow d8 is measured d8

Once the s4 and d4 flows are activated, the sum flow s4d4 is measured

E’ uguale a fase 4 : basta cambiare gli indici per calcolare in fase 8 εr(s8) e εr(d8)

## Phase 15

It seems arriving a further difficulty, but it’s not : the comparison is not between groups with the same total capillaries number, but two groups have 8 capillaries and the bigger group have 15.

It’s enough to include in the equations a corrective factor 15/16

[s8d8-εr(s8)*(s8′)-εr(d8)*(d8′)] * 15/16 =s15- εr(s15)*s15 [s8d8-εr(s8)*(s8′)-εr(d8)*(d8′)] * 15/16 =d15- εr(d15)*d15

## Final considerations

Repeating different runs of the complete procedure is prossible to observe very low variance not specially on the measured flow values, but mainly on the calculated relative deviations : this is a confirmation of reliability. Another important point is the constant high resolution of measured flows and calculated relative deviations, not depending on flow size.

Beyond these observations, it’s normal the fact that who spent his life promoting without conditions the traceability principle, can be sceptical about this procedure where nothing is traceable. That’s normal.