# NDIR gas sensor calibration

1. Aug 2, 2010

### nano241

1. The problem statement, all variables and given/known data
I am looking for help and information to calibrate a NDIR co2 gas sensor for temperature and pressure compensation using the beers law extension coefficients.I have found some limited information through going through the web.
This is straight through gas cell made in the lab with component parts, light source, aluminium cell, dual pyroelectric detector with CO2 and reference filters. It was not a bought in sensor but one from a project passed onto me to continue with little documentation.

I am aware that there are 2 types of calibration for temperature:
One at zero gas concentration to compensate for zero temperature drift of the sensor.
One for span calibration which is calibrating the sensor at the span concentration eg 2% for different temperatures.

Then there is pressure compensation also as according to the ideal gas law PV = nRT changes in pressure will cause changes in the concentration of a measured gas.

2. Relevant equations
Beers Law: I/Io = exp(-ecl)
I/Io is the normalised Transmission which in a dual pyroelectric detector is
(active detector @ measurement)/ (I/Io zero gas * reference @ measurement)
NT = 1 - Normalised Absorption

Beers law is not valid for NDIR sensors at higher concentrations due to the bandwidth of the filter.
So beers law extension: NA = Span(1-exp(-aC^n)
Span = NA/(1-exp(-aC^N)
NA: normalised absorption = 1-NT
C is gas concentration
a and n are the linearisation absorption coefficients.

Temperature Calibration coefficients:
Zero temperature calibration coefficients:
Zcorr = Z cal (a(T-Tcal)+1)
=> Zcor/Zcal = a(T-Tcal) +1
Zcorr: Zero correction Normalised Transmission which should be 1 at zero gas
Zcal : Normlised transmission at zero gas concentration
a: alpha compensation coefficient
T: Measured temperature in cell
Tcal: Measured Temperature in cell at calibration temp (20C or 293K)

Span temperature calibration coeff. ---Unsure if this is exaxtly correct.
Scorr = Scal(1+b(T-Tcal)
Scorr/Scal = b(T-Tcal)+1

Scorr: Span correction for measured temperature at span concentration
Scal: Span at calibration temperature span concentration
b: SPan calibration coefficient
T: Temperature measured in cell
Tcal: Temperature at calibration.

Ideal Gas Law: PV = nRT

3. The attempt at a solution
I am looking to calibrate a CO2 NDIR gas sensor so it will compensate for temperature changes in the sensor. Below is how I think it should be carried out from the above equations but I am not certain and am missing some information on pressure calibration.

1. Zero temperature coefficient calibration.
I think this is to be done as follows:
Firstly at 0 gas concentration measure the Normalised Transmission of the sensor for different temperatures say 60C, 20C, 0C and -20 C. The calibration temperature is to be 20 C = 293 K.
From Zcorr/Zcal = a(T-Tcal)+1 is an equation of a line with a as the slope.
I think the Zcorr Normalised Transmission is 1 as this is the Normlised Transmission at 0 gas.
From the data measured at the different temperatures line can be graphed with Zcor/Zcal as the y axis and T-Tcal as the x axis.
The slope of that line will be the a the zero calibration cefficient from which Zcor, the corrected normalised transmission can be calculated to correct for the concentration measurement at a different temperature to the calibration temperature.

How correct is this???

2. Span temperature correction coefficient
I am uncertain as to the correct Span correction equatio but was given the above equation as one option.
The procedure to calculate the span temperature correction coefficient is similar to the zero.
The sensor is exposed to 5% span gas concentration and the Normlised Transmission measured for different temperatures like 60c, 20c, 0c and -20c. using equation Span = NA/(1-exp(-aC^n) the span is calculated for each of the measurements at the different temperatures.
Then from the data the slope of Span Corr/Spancal (y-axis) vs T-Tcal (x-axis) gives us b the Span temperature calibration which gives us the SPan corr value to be used in the new concentration equation
C=[-ln(1-(1-NTcal)/Spancal)/a]^1/n
The problem is that according to the ideal gas law the a change in temperature causes a change in gas concentration so how to accomadate that into the above span temperature correction.
One way I thought of is that from the calibration temperature use the ideal gas law to recalculate the concentration. eg 1/n1T1 = 1/n2T2 => n2= (n1*T1)/T2

Then use the new concentration in the Span calculation Span = NA/1-exp(-aC^n)

Does anyone have any suggestions or know how this should be done?

Finally the gas concentration also changes due to pressure but I do not know how to compensate for this. I was thinking that you recalculate the concentration for the change in pressure and take this as a ratio of the calibration pressure which is 1 bar and multiply it by the concentration which is calibrated to temperature???

ANy help information or thoughts would be much appriciated.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution