Operation Manual HORIBA APDA-371
Particulate Monitor
Date:
April, 2010
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________
HORIBA Europe GmbH, Julius-Kronenberg-Str. 9, D-42799 Leichlingen, Telefon: +49(0)2175-8978-0, Fax: +49(0)2175-8978-50
Page 5
Equation 4
=
I
I
ln
g
cm
∆
t(min)
µ
min
liter
Q
)
A(cm
10
m
µ
g
c
0
2
2
6
3
The key to the success of the beta attenuation monitor is due in part to the fact that
µ
, the absorption cross-section, is
almost insensitive to the nature of the matter being measured. This makes the APDA-371 very insensitive to the
chemical composition of the material being collected.
It is instructive to perform a conventional propagation of errors analysis on Equation 4. Doing so, one can develop an
equation for the relative measurement error (
σ
c
/c) as a function of the uncertainty in each of the parameters comprising
Equation 4. This leads to Equation 5.
Equation 5
2
0
2
0
2
I
2
0
2
2
I
2
2
µ
2
2
t
2
2
Q
2
2
A
c
I
I
ln
I
σ
I
I
ln
I
σ
µ
σ
t
σ
Q
σ
A
σ
c
σ
0
−
+
+
+
+
=
Inspection of Equation 5 reveals several things. The relative uncertainty of the measurement (
σ
c
/c) is decreased
(improved) by increasing the cross sectional area of the filter tape (A), the flow rate (Q), the sampling time (t), the
absorption cross-section (
µ
), I and I
0
.
In practice, the uncertainty associated with the filter area (
σ
A
/A), may be minimized by ensuring that the tape is in
exactly the same position during the I
0
measurement as in the I measurement phase. Careful design of the shuttle and
tape control mechanisms inside of the APDA-371 results in minimal error here.
The uncertainty in the flow rate (
σ
Q
/Q) may be minimized by properly controlling the flow of the instrument. For APDA-
371 units with a manual flow valve, this value is on the order of
±
3%. For APDA-371 units equipped with the mass flow
controller device, (
σ
Q
/Q) decreases to
±
1%.
The relative error due to the uncertainly in the absorption cross section (
σ
µ
/
µ
), is due to its slight variation as a function
of the chemical composition of the matter being monitored. Generally, this relative error is on the order of
±
2-3%, with
judicious selection of the calibrated value of
µ
.
The uncertainty associated with the measurement of I and I
0
has to do with the physical nature of the process leading to
the emission of beta particles from the decay of
14
C. This process follows Poisson statistics. Poisson statistics show the
uncertainty in the measurement of I (
σ
I
/I) and I
0
(
σ
I0
/I
0
) are minimized by increasing the sampling time. Mathematical
analysis shows that doubling the sampling time and hence the measured intensity of I or I
0
will reduce the uncertainty of
the measurement by a factor of 1.41 (square root of 2).
11.1
Converting Data Between EPA Standard and Actual Conditions
As described in this manual, the APDA-371 can obtain concentration data using either actual or standard values for
ambient temperature and pressure. In some cases, it is necessary to convert past concentration data collected in
standard conditions to actual conditions, or the other way around. Note: temperature is in degrees Kelvin (°C+273) and
pressure is in mmHg.
Equation 6
Equation 6 can be used to calculate the standard concentration (C
std
) from the ambient concentration (C
amb
) data using
ambient barometric pressure and temperature data (P
amb
and T
amb
) from the same time period in which the ambient
concentration was recorded. P
std
and T
std
are the values of standard barometric pressure and standard ambient
C
std
= C
amb
* (P
std
/ P
amb
) * (T
amb
/ T
std
)