# Patent

## Title
Gas sensor and method for determining a concentration of gas in a two-component mixture

## Abstract

The described sensor allows determination of the concentration of a gas in a two-component mixture at variable pressure by measuring the diffusivity and the thermal conductivity. The sensor is provided to alternately heat the membrane of a thermally conductive cell and allow it to cool such that the temperature TM of the membrane passes from a first stable value to a second stable value and vice versa via a transient mode. The cell produces a signal representative of the temperature TM of the membrane and the sensor extracts from the signal a first and a second parameter that respectively relate to said first stable value and said transient mode of the signal. A value of the concentration of said gas and of the pressure of said two-mixture is calculated from these two parameters.

## Background
CROSS REFERENCE TO RELATED APPLICATIONS
This is a divisional of U.S. patent application Ser. No. 13/623,548, filed Sep. 20, 2012, which claims priority from EP Application Nos. 11183314.1 filed Sep. 29, 2011 and 12163201.2 filed Apr. 4, 2012. The entire disclosures of the prior applications are considered part of the disclosure of the accompanying divisional application, and are hereby incorporated by reference.


BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to the field of thermal gas sensors. More specifically, it relates to a thermal gas sensor for determining a concentration of gas in a two-component mixture at variable pressure. It also relates to a method for determining a concentration of gas in a two-component mixture of variable concentration.
2. Background
Thermal gas sensors take advantage of thermal conductivity properties of the gases to provide information on the nature of a gas or its concentration in a gaseous mixture. The thermal conductivity λ of a gas is its capacity to transport heat under the effect of a temperature gradient. It is an intrinsic magnitude of a gas at a given pressure and temperature and this is why its measurement is able to provide an indication of the composition of a gaseous mixture. Thermal gas sensors are used in particular for measuring the concentration of hydrogen (H2) in another gas such as oxygen (O2), nitrogen (N2), argon (Ar), carbon dioxide (CO2) or even air (assuming that it is of fixed composition), since hydrogen differs greatly from other gases because of its high thermal conductivity in comparison to that of heavier molecules. The following values are given for information purposes:
λhydrogen=0.84 Wm−1K−1
λair=0.012 Wm−1K−1.
Thermal gas sensors generally have an electrically insulating membrane of low thermal inertia, on which devices for heating the membrane and devices for measuring its temperature are arranged. The membrane is conventionally formed from a thin layer of silicon oxide or nitride deposited onto a silicon substrate, which is locally etched to the rear face of the membrane such that a gas flux can circulate on either side thereof. The heating devices and devices for measuring the temperature respectively comprise a first and a second electrical resistance formed by metal lines meandering over the front face of the membrane. The metal used for the temperature measuring devices has a variable resistance as a function of the temperature, such that measuring the voltage at its terminals enables the temperature of the membrane to be determined. When this latter is heated by the heating devices, its temperature rests at a stable value that is dependent on the thermal conductivity of the gaseous mixture or the ambient gas. As a result of this, the measurement of the temperature of the membrane provides an indication of the nature of the ambient gas or of the composition of the gaseous mixture. Reference is made to DE4228484 for more details on the structure and operation of such a gas sensor.
A gas sensor of the type described above allows measurement of a variable of a two-component gaseous mixture, i.e. the concentration of one of the gases, on the basis of one parameter: the temperature of a membrane in physical contact with said mixture. It assists in particular in determining the concentration of hydrogen in another gas, as explained above. There is considerable interest in determining the proportion of hydrogen in another gas with precision, since what is at stake in this case concerns the level of safety of installations and personnel. In fact, it is known that hydrogen forms a highly explosive mixture with oxygen, even at low concentrations. The same applies with air, which contains approximately twenty per cent oxygen. A thermal gas sensor provides such an indication at low cost and space requirement, hence its significant technical interest.
However, the measurement of a variable of a two-component gaseous mixture, in the case in point the concentration of one of the gases, on the basis of one parameter: the temperature of a membrane of low thermal inertia, is only possible if all the other variables of the mixture are constant. In particular, the pressure of the gaseous mixture has a significant influence on its conductivity. At variable pressure, it becomes impossible to determine the concentration of a gas in a two-component mixture on the basis of a single temperature measurement of the membrane.
Such a situation is encountered, for example, within an electrolyser unit. These devices are intended in particular for the production of gaseous hydrogen from water. These are currently the subject of significant developments since they offer a clean energy alternative to fossil fuels. Application EP 2 048 759, for example, describes a domestic installation for the production and storage of gaseous hydrogen using an electrolyser supplied with power by a photovoltaic installation. The hydrogen is then used as fuel in a fuel cell fitted, for example, in an electric vehicle.
In an electrolyser of the type described in application EP 2 048 759 hydrogen is produced from liquid water by means of an anode and a cathode. In a variant, the electrolyser is formed by an assembly of electrolytic cells, each of which having an anode and a cathode. Such a device is described in the patent document GB 1,145,751. Whatever the structure of the electrolyser, hydrogen is produced on the cathode side, while oxygen is produced on the anode side. The accumulation of these gases during the production process, respectively on the cathode side and anode side, causes the pressure within the electrolyser to increase progressively up to a value in the order of ten to several tens of bars. Because of the risks of explosion of an oxygen-hydrogen mixture, it is necessary to detect any presence of hydrogen in the oxygen and vice versa over the entire operating pressure range of the electrolyser. To achieve this and because of the above-mentioned limitation of thermal gas sensors, a pressure sensor is generally added to the gas sensor installed in the electrolyser. It is then possible to combine pressure and temperature measurements to get up to the concentration of gas to be determined. However, this solution increases the cost of this type of detection significantly, which represents a major disadvantage for a domestic installation.
SUMMARY OF THE INVENTION
The aim of the present invention is to remedy this disadvantage by proposing a thermal gas sensor that is able to determine the concentration of a gas in a two-component mixture at variable pressure. More specifically, the present invention relates to a sensor for determining the concentration of a gas in a two-component mixture at variable pressure as disclosed and claimed herein.
Because of its features and in particular, as described, the choice of frequency f of the current source supplying the heating devices, the gas sensor according to the invention allows measurement not of one single parameter of the gaseous mixture, i.e. a stable temperature in continuous mode, but two parameters of the gaseous system, one associated with its statics and the other associated with its dynamics. These two parameters inserted into a mathematical function established for this purpose allow determination of not one variable of the gaseous mixture, but two, e.g. the concentration of one of the gases and the pressure of the mixture. Measurement of the pressure of the gaseous mixture by an independent device attached to the gas sensor becomes superfluous.
The present invention also relates to a method for determining the concentration of a gas in a two-component mixture at variable pressure by means of a gas sensor comprising a step of measuring a first characteristic parameter of the conduction of the two-component mixture, a step of measuring a second characteristic parameter of the diffusivity of the two-component mixture and a step of calculating a value of the concentration of said gas and the pressure of said two-component mixture from said parameters with the assistance of a previously established mathematical function and characteristic coefficients of the sensor.



BRIEF DESCRIPTION OF THE DRAWINGS
Other features and advantages of the present invention will become evident upon reading the following description provided solely by way of example with reference to the attached drawings:
FIG. 1 is a sectional view of the measurement cell of a gas sensor according to the invention; and
FIG. 2 shows a basic operational diagram of the sensor according to the invention; and
FIG. 3 shows an example of a measurement signal of said sensor.



DETAILED DESCRIPTION OF THE INVENTION
As an initial observation, it is mentioned that the gas sensor according to the invention is intended in particular to measure hydrogen in oxygen for the reasons outlined above. However, its operating principle for determining variables of a gaseous mixture can be extended to any two-component mixture. Furthermore one of the two gases can be air, assuming that its composition is constant. In the following description it will be noted that % H and % O are respectively the proportions of hydrogen and oxygen forming the two-component mixture to be analysed and P is its pressure, and there will be no further reference to another gas.
The thermal gas sensor according to the invention conventionally comprises a measurement cell intended to be immersed into two-component oxygen/hydrogen mixture to be analysed, shown schematically in FIG. 1 and given the overall reference 1. The cell 1 comprises a rigid base 10 that has an opening 11 in its centre and is covered by an electrically and thermally insulating membrane 12 of low thermal inertia. The opening 11 allows an ambient gas to circulate and transport heat on either side of the membrane 12. The effect of the conductivity of the gas on the temperature of the membrane 12 thus outweighs the cooling associated with other physical phenomena such as heat radiation or conduction through the base 10. Heating devices 13 are arranged on the membrane 12 at the level of the opening 11, while measuring devices 14 for the temperature TM of the membrane 12 are situated in the vicinity of the heating devices 13. Measuring devices 15 for the ambient temperature TA are arranged spaced from the heating devices 13 so as not to be subjected to their effect.
In a particularly advantageous embodiment the cell 1 is made from a sheet of silicon forming the rigid base 10 using production techniques for micromechanical devices well known to the person skilled in the art. The membrane 12 is formed from a layer of silicon nitride Si3N4 or silicon oxide SiO2 deposited on the sheet of silicon or obtained by thermal nitridation or oxidation. Its thickness is typically several hundreds of nanometres. The opening 11 is generally formed by chemical etching of the silicon sheet from its rear face after formation of the membrane 12. The heating devices 13 as well as the measuring devices 14 for the temperature TM of the membrane 12 are formed by metal lines meandering over the membrane 12 above the opening 11. The metal used to form the measuring devices 14 has a resistance RM that varies as a function of temperature in the known manner at a standard reference pressure. The relation linking the resistance RM to the temperature TM of the membrane 12 that is well known to the person skilled to the art has the following form:

RM=R0*(1+αTM)  (1)

in which the coefficient α is a characteristic of the metal forming the metal line 14: generally platinum, nickel or an alloy of these two metals. In the same way, the measuring devices 15 for the ambient temperature TA are formed from lines of metal, the resistance RA of which is thermo-variable. In a similar manner, the ambient temperature TA is associated with the value of the resistance RA by relation (1). A passivation layer 16 formed from a silicon oxide SiO2 or a silicon nitride Si3N4 covers the metal lines 14 and 15.

The cell 1 is powered by an alternating current source 20 shown schematically in FIG. 2 that supplies a square alternating current of frequency f to the heating devices 13. The frequency f lies in the range of between a few hertz and some tens of hertz, depending on the layout and size of the cell 1. Typically, it lies in the order of 20 hertz. It is selected to allow the heating devices 13 to heat and alternately cool the membrane 12 so that its temperature TM passes from a first stable value TH to a second stable value TB and vice versa via transient modes. This aspect of the gas sensor according to the invention will become clearer by looking at FIG. 3. The temperature TM of the membrane 12 is given by the measuring devices 14, which supply an analog signal representative of TM, for instance a value of the resistance RM of the metal line forming the measuring devices 14. Moreover, the ambient temperature TA is given by the measuring devices 15, which supply an analog signal representative of TA, for instance a value of the resistance RA of the metal line forming the measuring devices 15. It must be noted here that the temperature TM is a function of the ambient temperature TA and of the thermal conductivity λ of the ambient gas, which is itself a function of the ambient temperature TA and of the nature of said gas.

TM=f(TA, conductivity (TA, gas))  (2)

Consequently, the temperature TA of the membrane 12 must firstly be corrected in the first order of the effect of the ambient temperature TA in order to give information about the conductivity of the ambient gas. For this purpose, it is the ratio RM/RA that is output from the cell1, then processed by an electronic circuit 30 comprising a analog to digital converter 21, a controller 22, a memory module 23 and a time base 24.
The analog to digital converter 21 arranged at the output of the cell 1 transforms the analog signal RM/RA into a digital signal, which is processed by the controller 22. The ROM memory module 23 (read only memory) connected to the controller 22 stores a plurality of coefficients characteristic of the gas sensor necessary for processing the RM/RA signal. These coefficients will be explained below. The controller 22 is also connected to a time base 24 formed by a crystal and to the alternating current source 20, whose frequency f it controls.
We will now refer to FIG. 3 that shows the development of the temperature TM of the membrane 12, as measured by the resistance RM, and that of the supply current 1 for the heating devices 13 as a function of time. When it is heated by the heating devices 13 in the presence of a gaseous mixture of oxygen and hydrogen, the membrane 12 experiences a rise of its temperature TM to a high stable value TH measured by the measuring devices 14. The high value TH is dependent on the thermal conductivity of the surrounding gaseous mixture that transports the heat supplied by the heating devices 13 reasonably easily. When the heating devices 13 cease to heat the membrane 12, this cools to a low stable value TB that is substantially equal to the temperature of the ambient medium. Between the high TH and low TB stable values, the temperature TM of the membrane 12 passes through transient modes tHB and tBH of cooling and reheating respectively, which are principally determined by the thermal diffusivity of the surrounding gaseous mixture.
In contrast to thermal conductivity, which defines the behaviour of a gas in static mode, diffusivity characterises the capacity of the gas to progress from one temperature to another and determines its behaviour in dynamic mode. Like thermal conductivity, the diffusivity of the gaseous mix depends on the nature of the gases, their concentration and the ambient pressure, but in a very different manner. According to the invention, the pieces of information supplied by high stable temperature TH and by the transient cooling mode tHB are combined to determine the composition of the gaseous mixture, whatever its pressure.
In fact, numerous systematic measurements and tests conducted within the framework of the present invention have made it possible to show that the different variables of the gas to be analysed: % H, % O or P, are associated with the value TH and to the cooling gradient ptHB measured during the transient cooling mode tHB by simple mathematical functions, in which the above-mentioned coefficients play a part. It must be noted here that the cooling of the membrane 12 follows an exponential e−k/T law. The cooling tHB gradient ptHB is thus defined by the following function:

ptHB=d/dt(In((TH−TB)/(Ti−TB))  (3)

in which the points Ti, three in number, are measured at different intervals during the transient cooling mode tHB, for example, at 10, 14 and 18 ms of the point TH in the present case. It will be noted that the choice of the number of points Ti and of the time interval separating them depends on the layout of the cell 1 as well as numerous other parameters such as the nature of the gases forming the two-component mixture. Consequently, it does not follow a strict rule, but must be conducted empirically in order to take the gradient ptHB into consideration in the best way possible.

Once the calculation of the gradient ptHB has been conducted by the controller 22, the different variables of the oxygen/hydrogen gaseous mixture are provided by mathematical functions to be adapted as a function of the working conditions of the sensor according to the invention. These functions are quite complex, depending on whether the gas to be measured is hydrogen in oxygen or vice versa, or depending on the range of pressure of the gaseous mixture. In fact, hydrogen has a much higher thermal conductivity than oxygen. As a result of this, the high stable temperature TH is lower in the case of a gaseous mixture formed substantially of hydrogen than in the case of a gaseous mixture formed mainly of oxygen. The difference between TH and TB is therefore smaller and the accuracy of the measurement is therefore lower. On the other hand, a broad working pressure range causes greater variations in behaviour of the gaseous mixture than a low pressure range, and this must be taken into account in the calculation of the variables of the gaseous mixture.
In the following description, two mathematical functions are proposed that allow determination of the composition of the gaseous mixture respectively in a simple case and in a more complex case in point. The first case corresponds, for example, to a pressure range of 1 to 5 bar. The second case in point applies, for example, to the detection of a low quantity of oxygen in hydrogen over a pressure range of 1 to 20 bar. It is to be understood that not all the working conditions of the gas sensor according to the invention will be explained in full detail in this description, but the mathematical functions given below can be adapted and modified to correspond to multiple conditions of use of the gas sensor without departing from the framework of the invention.
A first example of working condition relates to the measurement of a concentration of hydrogen ranging from 0 to 2 per cent in oxygen over a pressure range varying from 0 to 5 bar. It has been determined by different calculations and tests that the pressure P and the proportion of hydrogen % H can be precisely represented by the following respective functions:

P=a*TH+b*TH2+c*ptHB+d*ptHB2+e*(TH/ptHB)+f  (4)

% H=A*TH+B*TH2+C*ptHB+D*ptHB2+E*(TH/ptHB)+F  (5)

in which coefficients a, b, c, d, e, f and A, B, C, D, E, F are characteristic of the gas sensor and are determined by a calibration procedure. Said calibration consists of measuring values TH and ptHB for three different pressure ranges and two different concentrations of hydrogen in the ranges of pressure and working hydrogen concentration, then by means of a solver minimising the differences between the measured and calculated values of P and % H. Equations (4) and (5) thus respectively deliver a hydrogen percentage value with an accuracy of 500 ppm and a pressure value with an accuracy of 0.2 bar.

A second example of working condition relates to the measurement of a concentration of oxygen ranging from 0 to 1 per cent in hydrogen over a pressure range varying from 0 to 20 bar. In this case, the pressure P and the proportion of oxygen % O can be precisely represented by the following respective functions:

P=g*TH+h*TH2+i*ptHB+j*ptHB2+k*(TH/ptHB)+1  (6)

% O=G*TH+H*ptHB+I*ptHB2+J*(TH/ptHB)+K*(TA−Tref)*(P−Pref)+L*(TA−Tref)*(P−Pref)2+M  (7)

in which coefficients g, h, i, j, k, l and G, H, I, J, K, L, M are determined as above, TA is the ambient temperature measured by the measuring devices 15, Tref is the reference temperature at which the calibration points are conducted and Pref is the reference pressure at which the variation of resistance RM is measured as a function of the temperature. This approach allows the effects of the ambient temperature TA to be taken into account on the dependence curves of the conductivity of the gas as a function of pressure. This is second-order correction of the temperature. It also takes into account the effects of pressure on the temperature dependence of the measurement resistances 14 and 15. The thus improved equation (7) delivers a value of the proportion of hydrogen with an accuracy of 600 ppm over the entire range of working pressure and the pressure is given by equation (6) with an accuracy of 0.5 bar.
A thermal gas sensor for determining a concentration of gas in a two-component mixture at variable pressure has thus been described. It is understood that the gas sensor according to the invention is not restricted to the embodiments that have just been described and various simple modifications and variants can be envisaged by the person skilled in the art without departing from the framework of the invention as defined in the attached claims.
In particular, the parameters used by the gas sensor according to the invention are the high stable temperature TH and the cooling gradient ptHB. In a particular context, a person skilled in the art could have cause to choose other parameters such as the high stable temperature TH and the gradient for reheating the membrane ptBH without involving inventive activity. The mathematical functions delivering the variables of the system from measured parameters would thus be potentially significantly different from the functions explained above.
It must also be mentioned that other means for heating the membrane 12 or for measuring its temperature are part of the framework of the present invention. For example, it is known that the temperature of a membrane immersed in a gas to be analysed can be delivered by a diode rather than by a metal line with thermo-variable resistance. Moreover, it is conceivable that another element of low thermal inertia such as a filament can be used in place of a membrane.
Finally, it is noted that the present invention relates to a method for determining the concentration of a gas in a two-component mixture at variable pressure. Said method is based on the measurement of a parameter in stable mode and a parameter in transient mode of the gaseous mixture and on the determination of a mathematical function to calculate the variables of the gaseous mixture from these parameters. A gas sensor has been described above that is particularly well suited to measuring these values and for application of this method. However, the method according to the invention is not restricted to such a sensor, but can be extended to any sensor that delivers the above-mentioned measurements by any appropriate means.

## Claims

1. A method for determining the concentration of a gas in a two-component mixture at variable pressure comprising:
measuring, by a gas sensor, a first characteristic parameter of conduction of said two-component mixture, the first parameter being representative of a high temperature TH of an element of the sensor in a stable mode,
measuring, by the gas sensor, a second characteristic parameter of the diffusivity of said two-component mixture, the second parameter being representative of a cooling rate ptHB of the element of the senor in a transient cooling mode tHB, and
calculating, by a circuit of the gas sensor, a value of the concentration of said gas and the pressure of said two-component mixture from said parameters with the assistance of a mathematical function and characteristic coefficients of said sensor,
outputting, by the gas sensor, the calculated value of the concentration of said gas;
wherein said first and second parameters being measured in alternating mode at a given frequency (f),
wherein the gas sensor outputs the calculated value, of the gas concentration to an electrolyzer to determine production of energy fuel based at least in part on the calculated value.

2. The method according to claim 1, wherein said cooling rate ptHB of an element of the sensor is given by the following function:


ptHB=d/dt(In((TH−TB)/(Ti−TB))

in which the points Ti are measured at different intervals during the transient cooling mode tHB of said sensor.

3. A method according to claim 2, wherein the concentration of a gas of said two-component mixture is a polynomial function of said parameters representative of the high stable temperature TH and the cooling rate ptHB of the following type:


A*TH+B*TH2+C*ptHB+D*ptHB2+E*(TH/ptHB)+F

in which A, B, C, D, E and F are included in said characteristic coefficients of the sensor and are obtained by calibration of said sensor.

4. The method according to claim 2, wherein the pressure of said two-component mixture is a polynomial function of said parameters representative of the high stable temperature TH and the cooling rate ptHB of the following type:


a*TH+b*TH2+c*ptHB+d*ptHB2+e*(TH/ptHB)+f

in which a, b, c, d, e and f are included in said characteristic coefficients of the sensor and are obtained by calibration of said sensor.

5. The method according to claim 2, wherein the concentration of a gas of said two-component mixture is a polynomial function of said parameters representative of the high stable temperature TH, of the cooling rate ptHB, of the ambient temperature TA, of a reference temperature Tref and of a reference pressure Pref of the following type:


G*TH+H*ptHB+I*ptHB2+J*(TH/ptHB)+K*(TA−Tref)*(P−Pref)+L*(TA−Tref)*(P−Pref)2+M

in which G, H, I, J, K, L and M are included in said characteristic coefficients of the sensor and are obtained by calibration of said sensor, and in which Tref is the reference temperature at which the calibration is conducted and Pref is the reference pressure at which said. signal is calibrated as a function of the membrane.

6. The method according to claim 1, wherein the electrolyzer is further configured to produce the energy fuel.

7. The method according to claim 1, wherein the gas sensor is located in the electrolyzer and the output value is analyzed by the electrolyzer to avoid explosion.

8. The method according to claim 1, further comprising, in response to the calculated value exceeding a safety value, controlling a production process of gas or fuel.

9. The method according to claim 1, wherein the two-component mixture comprises oxygen and hydrogen and wherein gas produced is supplied to a fuel cell.

10. A sensor configures to calculate a concentration of gas in a two-component mixture comprising:
a heater configured to heat and cool a membrane of a cell immersed in the two-component mixture;
a measurer configured to measure a first characteristic parameter of conduction of said two-component mixture, the first parameter being representative of a high temperature TH of the membrane of the cell immersed in the two-components mixture in the stable mode and configured to measure a second characteristic parameter of the diffusivity of said two-component mixture, the second parameter being representative of a cooling rate ptHB of the membrane of the cell immersed in the two-component mixture in a transient cooling mode tHB;
an electronic circuit configured to calculate a first value of the concentration of said gas and a second value representing pressure of said two-component mixture from said parameters with an assistance of a mathematical function and characteristic coefficients of said sensor; and
an alternating current source configured to supply alternating current of frequency to the heating device,
wherein said first and second parameters being measured by the measuring device in an alternating mode at a given frequency (f).

11. The sensor according to claim 10, wherein the electronic circuit calculates the first value of the concentration of said gas based on the calculated second value, the first and second characteristics measured by the measurer.