0~2000ppm Range and 232ppm Resolution

CO₂ Thermal Conductivity Sensors

Xiang Zheng Tu

 

Figure 1 shows a thermopile thermal conductivity sensor provided by POSIFA Microsystems Company. The sensor mainly comprises a silicon chip, a hot plate suspending over a cavity recessed into the silicon chip, a resistor and a thermopile both disposed on the hot plate. The resistor is heated by applying a square pulse voltage and the thermopile is used to measure the temperature difference between the hot plate and the silicon chip. The temperature difference depends upon the thermal conductivity of the gas or gas mixture filled in the cavity. Since the sensor is ultra miniature its thermal time constant is short enough to allow for heating the sensor to work with very narrow pulses of electricity. So the power consumption throughout sensor's operation is quite low.

Figure 2 shows measurement data for indoor air. The heating square pulse voltage is supplied by Agilent 8110A 150 MHz Pulse Generator. The square pulse voltage is chosen to have: period = 1s, width = 20ms and amplitude = 8.96V. The out voltage of the sensor is measured by a TDS Digitizing Oscilloscope, which is shown as 1.86mV.

Figure 3 shows measurement data for 40% carbon dioxide and 60% nitrogen.

The heating pulse voltage is maintained as the same. The out voltage of the sensor is shown as 1.924V which is higher than the out voltage measured for indoor air. 

Using the above measurement data the sensitivity of the thermopile thermal conductivity sensor for carbon dioxide in nitrogen or in indoor air can be calculated as 1.65mV/1%.

In order to determine the resolution of a practical sensor measurement system in terms of voltage, we have to make a few calculations.

·      Assume the system capable of making measurements across 0 to 5V range,

·      Using a18-bits A/D converter, and

·      Using an averaging technique for reducing the noise contribution from four counts to one count.

Therefore, the smallest theoretical change we can detect is 153μV or 232ppm carbon dioxide in nitrogen. 

Requirements for circuit design for natural gas calorific meters

Xiang Zheng Tu

The project is divided into two phases as:

·      The first phase is designing circuit for measuring the component mole fraction of a natural gas using POSIFA’s thermopile thermal conductivity sensors.  

·      The second phase is combining this circuit with an available mass flow measuring circuit. So as to obtain a complete circuit for natural gas calorific measurement.

A natural gas calorific meter comprises a MEMS thermal flow sensor and a MEMS thermopile thermal conductivity sensor which are provided by POSIFA Microsystems Company. The thermal flow sensor measures natural gas mass flow. A natural gas is a naturally occurring gas mixture, consisting of methane, ethane, propane and nitrogen. The heating value of a natural gas changes with its composition changes. The thermopile thermal conductivity sensors measure the component gas mole fraction in the natural gas flow. With the measured natural gas mass flow rate and component mole fraction the natural gas calorific flow rate and total calorific value can be calculated and displayed accordingly.

The component gas mole fraction of a natural gas can be measured based on the fact that the temperature curve of each component gas thermal conductivity coefficient is unique for each one, but highly correlated. A quaternary linear regression can be used to model the relationship between two or more explanatory variables and a response variable of a natural gas system by fitting a linear equation to observed data.

The thermopile thermal conductivity sensor is configured to have a polysilicon resistor used as heater (resistance = 250 to 350 Ω) and a thermopile used as temperature difference detector (resistance ~200 kΩ). In order to establish a quaternary linear system the heater must be driven using three square pulse voltage steps V₁, V₂, V₃.  The square pulse voltage can be shown as: 

After driving the heater a temperature difference between the hot junctions and cold junctions of the thermopile is established and a corresponding thermopile voltage is generated as:

Three square pulse voltages are used to successively heat the heater in the way as:

With resulting thermopile voltages a quaternary linear regression can be obtained as:

Y₁ =b₁₀ +b₁₁ N_Ethane +b₁₂ N_Propone +b₁₃ N_Nitrigen                     (1)

Y₂ =b₂₀ +b₂₁ N_Ethane +b₂₂ N_Propone +b₂₃ N_Nitrigen                      (2)

Y₃ =b₃₀ +b₃₁ N_Ethane +b₃₂ N_Propone +b₃₃ N_Nitrigen                      (3)

And an identity as

x_Methane +x_Ethane +x_Propone  +x_Nitrigen=1                                     (4)      

Where Y₁, Y₂ and Y₃ are the measured thermopile voltages when the heater is driven By 5, 7, and 9V square pulse voltages respectively, b₁₀ through b₃₃ are the parameters of the quaternary linear regression equation, which are determined by several experimental measurements, and N_Methane,  N_Ethane,,  N_Propone ,  N_Nitrigen  are the mole fraction of methane, ethane, propane, nitrogen.

With the measured values of Y₁, Y₂, Y₃, and the values obtained by fitting parameters b₀₁ through β₃₄, the values of N_Methane,  N_Ethane,,  N_Propone ,  N_Nitrigen  can be calculated by solving the equations (1) through (4).

A digital processing algorithm can also be build based on the equations (1) through (4). Using the obtained algorithm and the related program the component gas mole fraction of a natural gas coming from any different sources can be determined by operating a microcontroller.

                            

With the purpose of canceling the offset of the thermopile voltage of a thermopile thermal conductivity sensor a differential preamplifier is configured to have a sealed thermopile thermal conductivity sensor used as a reference input voltage. The sealed sensor may be filled with pure methane gas but not allowed to contact with natural gas to be measured. So its thermopile voltage will not change with the measured natural gas. Since the thermopile voltage of the exposed thermopile thermal conductivity sensor not only comprises natural gas signal and but also pure natural gas signal. After differential amplifying all common model signals will be canceled. That means the output of the amplifier should be no offset, no temperature drift and no noise. 

In the second phase the natural gas composition measurement circuit is incorporated with an available natural gas flow measurement circuit. The combined circuit is so called natural gas calorific measurement circuit.

Heating value of a natural gas can be calculated as:

Heating value = ( ṁ N_MethaneM_Methane/M_Mix) (HV_Methane) + ( ṁ N_EthaneM_Etane/M_Mix) (HV_Ethane)

+ ( ṁ N_PropaneM_Propane/M_Mix) (HV_Propane)                                          (5)                                                

Where: HV_n = heating value of natural gas component n, in BTU/SCF
N_n = mole or volume fraction of natural gas component n. 

ṁ = mass flow rate.

M_n = natural gas component mole quality.

M_Mix = natural gas average quality.

The following table shows the heating value of natural component gas: