Gas measurement device and measurement method thereof

Abstract

A gas measurement device measures gas using a gas sensor including a sense resistance exposed to the gas and a reference resistance not exposed to the gas. The gas measurement device applies a first current value and a second current value to the sensor. A detector functions to detect a first resistance variation and a second resistance variation of the sense resistance exposed to the gas with respect to the reference resistance as a function of the first current value and the second current value, respectively. The resistance variation dependent on relative humidity is then determined as a function of the first and second resistance variations and a first constant. The resistance variation dependent on gas content is then determined as a function of the first and second resistance variations and a second (different) constant.

Description

TECHNICAL FIELD

The present disclosure relates to a gas measurement device and measurement method.

BACKGROUND

A thermal conductivity detector (TCD) is well known in the state of the art. This is an environmental sensor device widely used for the measurement of the amount of gas in the environment. The operation is based on the fact that each gas has an inherent thermal conductivity and a filament (thermal resistor) changes its temperature as a function of the amount of gas that surrounds it. The most appropriate sensing element shape is that of a suspended thin finger, for which the temperature of the central part can locally reach even values of several hundred degrees. The feature that the finger is totally suspended allows for enhancing the amount of heat exchange with the gas in which it is immersed. The warming effect of the suspended finger is induced through an electrical stress of the sensor, that is by the flow of the current through the finger. The sensor is able to better discriminate the gases whose conductivity is much different than normal air (roughly nitrogen N₂ (79%), oxygen O₂ (19%), carbon dioxide CO₂ (0.04%), plus other gases with negligible quantities: for example the carbon oxide CO is a few ppm).

When a current flows through the finger, the value of the resistance of the finger changes. The measurement of the resistance value allows for measuring the conductivity of the gas mixture which depends of the molar fraction of the gas of interest.

However, it is difficult in principle to discriminate which gas is mainly responsible for the conductivity variation of the mixture of gas. For example, carbon dioxide CO₂ has a lower thermal conductivity than dry air, therefore if its percentage increases inside the mixture, this will raise the temperature of the sensor with a consequent increase of the value of the measured resistance.

The TCD sensor operates in accordance with the thermodynamic equilibrium among heat generated by the current flow, heat exchange with the material of which the sensor is made (e.g. polysilicon crystalline), and heat exchange with the gas mixture surrounding it. The ambient temperature determines the equilibrium value of the sensor in standard dry air. To take into account and compensate the variation of ambient temperature a Wheatstone bridge as the sensor structure could be used. The reference branches of the bridge are of the same nature and positioned in the vicinity of the sensor so as to be sensitive to the same way to changes in ambient temperature, with the difference that these branches will not be exposed to the mixture of gas as is the sensor.

The Relative Humidity (RH) is the amount of water vapor (gas) present in the environment compared to a saturated environment in the same conditions of pressure and temperature. The thermal conductivity of water vapor is much larger than the dry air therefore an increase in relative humidity produces a lowering of the temperature of the sensor with a consequent reduction of the value of the measured resistance. The contribution of the RH value of the measured resistance could be 1/10 compared to the change of resistance in the presence of carbon dioxide CO₂, therefore, this is a parameter to measure and correct. Typically the correction is made by means of a dedicated sensor for the measurement of the RH.

SUMMARY

One aspect of the present disclosure is to provide a gas measurement device of simple architecture.

One aspect of the present disclosure is a gas measurement device for measuring gas by means of a gas sensor comprising at least one resistance exposed to at least one gas and at least one reference resistance not exposed to the gas, said gas measurement device comprising: a control device configured to manage the gas sensor so that the gas sensor receives at least a first current value and a second current value, a detector to detecting a first resistance variation and a second resistance variation of the resistance exposed to the gas with respect to the reference resistance as a function of the first current value and the second current value respectively, and a calculation circuit configured to calculate at least a first and a second equations wherein the first equation is given by the difference between the first resistance variation multiplied by a first constant and the second resistance variation while the second equation is given by the difference between the first resistance variation multiplied by a second constant and the second resistance variation, the first constant and the second constant having different values.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the present disclosure, a preferred embodiment thereof is now described, purely by way of non-limiting example and with reference to the annexed drawings, wherein:

FIG. 1 shows a block diagram of a measurement apparatus comprising a gas sensor device and a gas measurement device according to the present disclosure;

FIG. 2 shows a more detailed block diagram of the gas measurement device according to the present disclosure;

FIGS. 3-5 show the waveforms of the resistance variations ΔR(Il), ΔR(Ih) as a function of the concentration of carbon dioxide CO₂ and the waveform of a resistance value as a function of the relative humidity RH;

FIG. 6 shows the waveforms of the resistance variation value as a function of the different concentrations of CO₂.

DETAILED DESCRIPTION

FIG. 1 shows a block diagram of a measurement apparatus comprising a gas sensor device 1, that is a TCD sensor, and a gas measurement device 100 according to the present disclosure.

The gas sensor device 1 comprises at least one variable resistance R2 exposed to the gas and a reference resistance R1 which is not exposed to the gas; the reference resistor R1 has the value of the resistance R2 at the condition of dry air and room temperature. The value of the resistance R2 varies when exposed to the gas, the humidity and the temperature. Preferably, the gas sensor device 1 is a Wheatstone bridge including a couple of reference resistors R1 and a couple of resistors R2 exposed to the gas; the use of a Wheatstone bridge allows for minimizing the dependence on the ambient temperature. The four connecting nodes A-D of the terminals of the resistances R1 and R2 of the Wheatstone bridge 1 are connectible respectively with a variable current generator 200, to ground GND and to the gas measurement device 100 able to receive the voltage signal at the output of the Wheatstone bridge 1.

The measurement device 100 (FIG. 1) comprises preferably a temperature sensor 102 in the case wherein it is necessary to provide a temperature compensation of the signals at the output of the sensor device 1. The measurement device 100 comprises preferably a multiplexer 101, configured to receive the output signal of the sensor device 1 or the output signal of the temperature sensor 102. The measurement device 100 comprises a device 103 configured to amplify the signal at the output of the multiplexer, an analog-to-digital converter 104 for converting the analog signals at the input into a digital signal at the output, a digital controller 105 for processing the signal deriving from the sensor device and an interface 106 for outputting the processed signal to the outside.

The measurement device 100 is shown in more detail in FIG. 2. The device 103 is preferably a low noise analog front end comprising the cascade of two fully differential switched-capacitor amplifiers configured to amplify the signal at the output of the multiplexer 101 and to compensate the offset of the gas sensor 1 or the temperature sensor 102. The low noise analog front end 103 makes use of both chopping and correlated double sampling techniques, which ensure offset canceling and low frequency noise filtering.

A managing device 109 manages the devices 101-106 and the variable current generator 210; the managing device 109 manages the timing of the low noise analog front end 103, the analog-to-digital converter 104 and the digital controller 105. The managing device comprises a clock generator 111 configured to send two different clock signals at different frequency, for example 1 Mhz and 40 Khz, to a phase generator 110 which receives the output of the bit register 112.

When a gas having a concentration m is inside the gas sensor 1 at a relative humidity n, the managing device 109 is configured to effectuate the following steps:

• • managing the variable current generator 210 to send a first current value Il to the gas sensor 1 and detect the resistance variation ΔR(Il) of the resistances R2 with respect to the reference resistances R1;
  • managing the variable current generator 210 to send a second current value Ih to the gas sensor 1 and detect the resistance variation ΔR(Ih) of the resistances R2 with respect to the reference resistances R1;
  • managing the digital controller 105 to calculate the resistance variation Δh depending only on the relative humidity variation by means of the following equation Δh=K1×ΔR(Il)−ΔR(Ih) and the resistance variation Δc depending only on the gas concentration variation by means of the following equation Δc=K2×ΔR(Il)−ΔR(Ih) wherein K1 and K2 are constants having different values. In this way the calculation of the above equations allow obtaining the indirect measure of the relative humidity alone, independently from the gas concentration, and of the gas concentration alone, independently from the relative humidity, and
  • managing the interface 106 to output the resistance variations Δh and Δc.

In the case wherein the concentrations of a first and a second gases need to be measured, the digital controller 105 is configured to:

• • manage the variable current generator 210 to send a first current value Il to the gas sensor 1 and detect the resistance variation ΔR(Il) of the resistances R2 with respect to the reference resistances R1;
  • manage the variable current generator 210 to send a second current value Ih to the gas sensor 1 and detect the resistance variation ΔR(Ih) of the resistances R2 with respect to the reference resistances R1;
  • manage the digital controller 105 to calculate the resistance variation Δc1 depending only on the concentration variation of the first gas by means of the following equation Δc1=K21×ΔR(Il)−ΔR(Ih)) and the resistance variation Δc2 depending only on the concentration variation of the second gas by means of the following equation Δc2=K22×ΔR(Il)−ΔR(Ih), wherein K21 and K22 are constants having different values. In this way the calculation of the above equations allow obtaining the indirect measure of the concentration of the first gas independently from the concentration of the second gas and vice versa, and
  • manage the interface 106 to output the resistance variations Δc1 and Δc2.

In FIGS. 3-5 the waveforms of the resistance variations ΔR(Il), ΔR(Ih) are shown wherein on the X axis the variation of the concentration of the gas is indicated while on the Y-axis the variation of the sensor resistance is indicated at the condition for a relative humidity RH=0, RH=30% and RH=60%. The further waveform is the resistance value Δh=K1×ΔR(Il)−ΔR(Ih) which is independent on the variation of the concentration of the gas and depends only on the relative humidity RH.

FIG. 6 show the resistance values Δc=K2×ΔR(Il)−ΔR(Ih) for gas concentrations m=0%, m=10% and m=20% which depend only on the concentration variation of the carbon dioxide CO₂ and are independent on the relative humidity RH.

Preferably the constants K1 and K2 have respectively the values of 1.827 and 2.165. A method for calculating the appropriate value of the constants K1 and K2 is now described.

The thermal conductivity of a gas mixture depends on the molar fraction of the gases of the mixture, on the conductivity of the gases and on the dynamic viscosity according to the Chapman-Enskog model.

In first approximation, starting from the Chapman-Enskog model (“The mathematical theory of non-uniform gases: an account of kinetic theory of viscosity, thermal conduction and diffusion in gases” S. Chapman, TG. Cowling 1970, incorporated by reference) and obtaining a linear equation, the thermal conductivity of a gas mixture is linearly proportional to the temperature and the concentration of gases of the mixture.

The resistance variation ΔR (that is the variation of the resistance R2 with respect to the reference resistance R1) is a linear function of both the concentration of the matters to be examined (the concentration of gas and the humidity or the concentrations of two gases) and the current flowing through the resistance R2, preferably, in the case wherein the sensor is a Wheatstone bridge, the resistance variation ΔR is a linear function of both the concentration of the matters to be examined and the current flowing through the bridge 1.

In fact, balancing and solving the equation for the thermoelectric equilibrium of the system comprising the bridge 1 and the gas mixture, the resulting temperature at the equilibrium is approximately a linear function of the concentrations of gas and humidity and of the current flowing through the bridge 1.

At the thermoelectric equilibrium it is necessary to consider the power dissipated by Joule effect on the resistance R2, P=R×I² wherein I is the current flowing through the bridge 1, and the amount of the heat exchange due to the thermal conductivity of the gas mixture,

$\frac{Q}{T}=K\times \frac{A}{\mathrm{dx}}\Delta T$ where A is the surface of the resistance R2, dx is the thickness of the resistance R2 and ΔT is the temperature variation; at the thermoelectric equilibrium it is obtained that the temperature variation ΔT is a linear function of the concentrations of gas and humidity and of the current flowing through the bridge 1 The resistance variation AR depends on the temperature variation ΔT according to the

ΔR=R0×(1+αΔT) where α is the thermal coefficient of the resistance and depends on the material of the resistive bridge and R0 is the resistance value at room temperature, therefore even the resistance variation ΔR, so as the temperature variation ΔT, is a linear function of the concentrations of gas and humidity and of the current flowing through the bridge 1. The resistance variation ΔR as linear function of the concentrations of gas and humidity and of the current flowing through the bridge 1 can be represented by the following equation ΔR=(a×I+b)×m+(c×I+d)×n wherein m is the concentration of gas, n is the concentration of humidity, I is the current flowing through the bridge 1 and a, b, c and d are parameters depending on the balance of the system which are determined by effectuating four calibration measurements with known gas and humidity concentrations and currents.

After determining the parameters a, b, c and d two measurements of the unknown mixture are effectuated with the unknown concentrations m and n and two different current values Il and Ih; solving said two equations and calculating the resistance variation as function of the current, that is ΔR(Il) and ΔR(Ih), the unknown values of the concentrations m and n are obtained.

Considering the generic equation ΔR=K×ΔR(Il)−AR(Ih), exist only two values K1 and K2 of K which allow the m and n concentration components to become null. The equation becomes: ΔR(K)=(a×(K×Il−Ih)+b×(K−1))×m+(c×(K×Il−Ih)+d×(K−1))×n and setting equal to zero the m and n concentration components the values

$K1=\frac{a\times \mathrm{Ih}+b}{a\times \mathrm{Il}+b}\mathrm{and}K2=\frac{c\times \mathrm{Ih}+d}{c\times \mathrm{Il}+d}$ are obtained. In this way each one of the results Δc(K2) and Δh(K1) depends on the concentration variations only of one of two unknown concentrations.

Claims

1. An apparatus for gas measurement, comprising: a gas sensor comprising a sensing resistance exposed to a first gas and a second gas and at least one reference resistance not exposed to the first and second gases,a current supply circuit configured to apply to the gas sensor a current having at least a first current value Il and a second current value Ih,a detector circuit configured to detect a first resistance variation ΔR(Il) of said sensing resistance exposed to the first and second gases with respect to the reference resistance as a function of the first current value Il and detect a second resistance variation ΔR(Ih) of the same sensing resistance exposed to the first and second gases with respect to the same reference resistance as a function of the second current value Ih, anda calculation circuit configured to calculate: a first resistance variation dependent on gas concentration of the first gas as a function of the first resistance variation ΔR(Il) and the second resistance variation ΔR(Ih) and a first constant K21 having a value by which the first resistance variation calculation is independent of concentration variation of the second gas; anda second resistance variation dependent on gas concentration of the second gas as a function of the first resistance variation ΔR(Il) and the second resistance variation ΔR(Ih) and a second constant K22 having a value by which the second resistance variation calculation is independent of concentration variation of the first gas;wherein the first constant K21 and the second constant K22 have different values.

2. The apparatus according to claim 1: wherein the first resistance variation is calculated as a function of a difference between the first resistance variation ΔR(Il) multiplied by the first constant K21 and the second resistance variation ΔR(Ih); andwherein the second resistance variation is calculated as a function of a difference between the first resistance variation ΔR(Il) multiplied by the second constant K22 and the second resistance variation ΔR(Ih).

3. The apparatus according to claim 2, wherein the calculation of the first resistance variation utilizes the following equation K21×ΔR(Il)−ΔR(Ih) and the calculation of the second resistance variation utilizes the following equation K22×ΔR(Il) −ΔR(Ih).