Determining the mixing ratio when mixing gases

Description

[0001] The invention relates to a method and a measuring device for measuring the mixing ratio of gases, even when the composition of the gases to be mixed changes over time, without having to adjust the calibration of the sensors used to determine the mixing ratio to the respective change. The invention further relates to a mixing device in which the method and / or the measuring device are used.

[0002] Mixing gases occurs in many areas of technology, be it in the process industry for the production of customer-specific gas mixtures, in medicine for adjusting different levels of anesthesia of the breathing gas, or in the natural gas industry to provide a consistent gas quality.

[0003] Consistent natural gas quality is ensured today, for example, by adjusting the calorific value depending on the origin of the natural gas: either by diluting it with air to a lower value or by enriching it with propane / butane to a higher value. The same applies to gases from renewable sources, such as biogas, which are adjusted in terms of calorific value or Wobbe index before being fed into the natural gas network in the manner described.

[0004] Among the newer trends is the blending of hydrogen with natural gas, with the hydrogen being produced from surplus electricity generated by renewable sources such as photovoltaics or wind power. Blending this hydrogen with natural gas allows it to be stored and transported using the existing gas infrastructure. At the same time, it is essential to know the exact amount of hydrogen in the natural gas at every point in the gas network to ensure safety, process compatibility, and / or the accuracy of gas billing.

[0005] Mixing techniques come in many variations, but fundamentally, two or more gas streams are always combined to form a single output stream. Both volumetric, mass-based, and analytical methods can be used to control and / or regulate the correct mixing ratio of the different gas streams. Volumetric methods (sum of input volume flows = output volume flow) can quickly become inaccurate if pressure or temperature changes during the mixing process. Mass-based methods are complex and require highly precise measuring instruments (scales, coriolismeters), while analytical methods for measuring the gas composition, at least in the output stream, also require expensive and sometimes non-real-time capable equipment such as gas chromatographs.

[0006] Another method for monitoring and / or controlling the mixing ratio is the determination of the proportions of two gas streams using sensors that measure a physical property of the gas mixture. Many variations of this method are available on the market. Most versions assume that the input gas streams are known and remain constant in composition throughout the mixing process. The sensors are calibrated differently for each mixing process and will deliver incorrect results if the composition of one of the gases being mixed changes.

[0007] Publication WO 02 / 40992 A1 describes a method for determining the mixture proportions of four gas components in a gas mixture. The method assumes that the three physical quantities being measured depend linearly on the mixture proportions of the components. A fourth equation results from the sum of the mixture proportions, which equals 100%. This linear system of equations contains twelve constants, which must be determined from known values ​​of the measured quantities using regression analysis.

[0008] EP 0 472 131 A1 describes a method for determining the concentration of a component of a multi-component gas mixture by measuring its thermal conductivity. In contrast to the method according to the present invention, the gases are not mixed, but rather separated for the determination, which can entail considerable effort for the separation apparatus.

[0009] EP2667276 discloses a method for determining the proportions of mixing two gases, wherein a physical property is measured in the mixed gas and in one or both of the gases using a sensor, and the proportion of one of the gases in the mixed gas is determined from the values ​​of the measured physical property.

[0010] The idea of ​​the invention is therefore to provide a method and a measuring device for determining the proportions of gases when mixing them, which, by measuring the physical properties of the gas flows, enables a cost-effective, real-time determination of the proportions of the gases to be mixed or of gas properties resulting from these proportions. Gas properties can be, for example, the calorific value, the Wobbe index, or the methane number.

[0011] This problem is solved by a method according to claim 1 and by a measuring device according to claim 13.

[0012] Physical gas properties can include, for example, the speed of sound, the refractive index, the diffusion coefficient, the optical absorption coefficient at a specific wavelength of electromagnetic radiation, the viscosity, the heat capacity, or the thermal conductivity. If the physical laws governing how a gas property of a mixture can be determined from the values ​​of the gases to be mixed are known, the mixing ratio can be calculated. Mixing two gases:

[0013] If the gas composition of the gases G1 and G2 to be mixed is known, then the physical properties of these gases can be determined, for example, from standardized calculation procedures or substance databases. PP 1 and PP 2 , based on which the measurement is taken. From the measured value for this physical property in the mixed gas, PP mix , Can one deduce the percentage composition C1 and C2 of gases G1 and G2 in the mixed gas? Fig. 1 ): PP mix = f PP 1 C 1 PP 2 C 2 und C 1 + C 2 = 100 %

[0014] At constant temperature and constant pressure before and after mixing, the function f(PP 1 ,C 1 ,PP 2 ,C 2 ) In the case of density ρ as a physical property, it depends linearly on the density and the proportions of the gases to be mixed: ρ mix = f ρ 1 C 1 ρ 2 C 2 = C 1 ⋅ ρ 1 + C 2 ⋅ ρ 2 C 1 + C 2 .

[0015] The denominator in equation (2) is equal to 1, so that with the condition C 1 +C 2 = 1 it can be solved for C 1 and C 2: C 1 = ρ mix − ρ 2 ρ 1 − ρ 2 und C 2 = ρ 1 − ρ mix ρ 1 − ρ 2 .

[0016] Since the mixing proportions C 1 and C If the composition of G1 and G2 is known, the composition of Gmix can be calculated. From Gmix, a variety of gas properties, such as calorific value or methane number, can then be determined using standardized calculation methods or substance databases.

[0017] In many applications, a base gas G1 is mixed with another, known component G2, such as in the processing of biogas for injection into the natural gas grid or, more recently, in the blending of hydrogen previously produced from renewable sources into natural gas. In both cases, the natural gas found in the local gas network is the base gas. Although the fluctuations in the composition of the natural gas are usually small, they can nevertheless result in an error in determining the blending rate C2 if only PP mix (= ρ mix ) is measured in the mixed gas. Be Δρ 1 the density change compared to the assumed density ρ 1 in the ground gas, so the ground gas has the density ρ 1 + Δρ 1 , the mixing rate is determined C 2eff as follows: C 2 eff = ρ 1 + Δ ρ 1 − ρ mix ρ 1 + Δ ρ 1 − ρ 2 .

[0018] Without knowledge of the change in the density of the base gas G1, C2 would have been calculated using equation (3) with a corresponding error compared to the RMS value in equation (4). The error is greater the more similar the values ​​are. ρ 1 , ρ 2 , and therefore also ρ mix are and amounts to within the limit ρ 1 - ρ 2 = ρ mix one hundred percent.

[0019] One object of the present invention is therefore to provide a method and a measuring device for determining the mixing proportions when mixing gases, which takes into account changes in the composition of one or more of the gases to be mixed and avoids errors in the determination of the mixing proportions that arise from such a change in the composition of the gases to be mixed.

[0020] This problem is solved according to the invention by the characterizing features of claim 1. Mixing three or more gases:

[0021] If n ≥3 gases are mixed together, the percentage proportions of the n gases can no longer be uniquely determined by determining only one physical property in the mixed gas.

[0022] In general, when mixing n gases, at least n - 1 physical properties must be considered. PP mix. 1 to PP mix.n-1 The properties of the mixed gas are measured to determine the proportions of the n gases in the mixed gas. If the n - 1 physical properties in the mixed gas are linearly dependent on the corresponding physical properties and the proportions of the n gases, a linear system of equations with n equations and n unknowns results: C 1 ⋅ PP 1.1 + C 2 ⋅ PP 2.1 + ⋯ + C n ⋅ PP n .1 = PP mix .1 C 1 ⋅ PP 1.2 + C 2 ⋅ PP 2.2 + ⋯ + C n ⋅ PP n .2 = PP mix .2 ⋮ ⋮ C 1 ⋅ PP 1 . n − 1 + C 2 ⋅ PP 2 . n − 1 + ⋯ + C n ⋅ PP n . n − 1 = PP mix . n − 1 C 1 + C 2 + ⋯ + C n = 1

[0023] If the n - 1 physical properties are linearly independent of each other, the system of equations has a unique solution for the mixture components C 1 , ..., C n .

[0024] The use of a second sensor in the ground gas to determine C 2eff In a preferred embodiment, the mixing ratio is directly output when two gases are mixed. In this case, the conversion from measured physical property to mixing ratio must be stored on the sensor. This is especially true for physical properties such as thermal conductivity λ, for which the mixing rule is non-linear and the measured signals must first be converted to a linear output signal using a calibration curve stored on the sensor. But how can changes in the base gas be taken into account if the calibration curves for mixing G2 with G1 are fixed on the sensor?

[0025] The idea of ​​the invention is to provide a method for taking into account changes in the gases to be mixed with respect to those physical properties used to calculate the mixing ratio during a mixing process. For this purpose, the calibration range for the physical property is chosen to be larger than would normally be expected for the gases to be mixed. This procedure is described in Fig. 4 shown: PP 2 is the known physical property of the mixing gas. The other end of the calibration scale is at PP min . PP min is positioned in such a way that the physical property PP 1 for the base gas for all expected changes in the base gas between PP min and PP 2 lies. This results in the dash-dotted figure diagonal as the calibration line CL. In the ground gas PP 1 measured with a second, identically calibrated sensor ( Fig. 2 ), resulting in an apparent mixing ratio C 2 (PP 1 ) for the mixing gas. C 2 (PP 1 ) This is an apparent mixture fraction, because the base gas before the mixture contains no added gas. In the mixture, PP mix determined, with which an apparent mixture fraction C 2 (PP mix ) is used for the mixing. To determine the effective mixing ratio. C 2eff To obtain the amount of the added gas in the mixture, it is best to set up the system of equations for the in Fig. 4 The effective measurement line ML eff, shown as a solid line, is shown (see also equation (1)): C 1 eff ⋅ PP 1 + C 2 eff ⋅ PP 2 = PP mix C 1 eff + C 2 eff = 1

[0026] The first equation can be multiplied on both sides by a non-zero factor s without this having any effect on the solution of the unknowns. C 1eff and C 2eff changes. The same applies to the second equation when multiplying by s · PP min : C 1 eff ⋅ s ⋅ PP 1 + C 2 eff ⋅ s ⋅ PP 2 = s ⋅ PP mix s ⋅ PP min ⋅ C 1 eff + s ⋅ PP min ⋅ C 2 eff = s ⋅ PP min

[0027] Similarly, in the first equation of the system of equations (7), the same value can be added or subtracted from both sides without this having any effect on the solution of the unknowns. C 1eff and C 2eff This changes. Therefore, if the left side of the second equation is subtracted from the left side of the first equation and the right side of the second equation is subtracted from the right side of the first equation, the system of equations (7) now reads C 1 eff ⋅ s ⋅ PP 1 − PP min + C 2 eff ⋅ s ⋅ PP 2 − PP min = s ⋅ PP mix − PP min C 1 eff + C 2 eff = 1

[0028] If the factor s := 100% / (PP 2 - PP min ) the slope of the calibration line CL corresponds to this, resulting in C 1 eff ⋅ C 2 PP 1 + C 2 eff ⋅ C 2 PP 2 = C 2 PP mix C 1 eff + C 2 eff = 1

[0029] i.e. a new system of equations with the unknowns C 1eff and C 2eff as a function of the apparent mixing proportions C 2 (PP 1 ),C 2 (PP 2 ) and C 2 (PP mix ). This can be easily determined by C 2eff dissolve: C 2 eff = C 2 PP mix − C 2 PP 1 C 2 PP 2 − C 2 PP 1 .

[0030] PP 1 and PP mix These are the physical properties of the respective gases measured by the two sensors in the base gas and in the mixture. C 2 (PP 2 ) = 100%, assuming the mixing gas G2 is known.

[0031] If the base gas G1 changes over time, the respective effective measurement line ML eff also changes. Fig. 4 . Nevertheless, the correct value for the addition of gas G2 to the base gas G1 is obtained using the apparent mixing ratios C 2 ( PP 1) and C2 ( PP mix). The two sensors are identical for the value range. PP min until PP 2 has been calibrated for the physical property PP.

[0032] The use of a third sensor in the mixing gas to determine C 2eff : The extension to the case where the mixing gas is also subject to certain fluctuations in composition is in Fig. 5 shown.

[0033] Additionally, a third sensor in the mixing gas is used to measure the physical properties before mixing. PP 2 measured (see Fig. 3 ).

[0034] All three sensors are designed for a range of values PP min until PP max calibrated in the same way for the physical property, so that PP 1 and PP 2 for all expected fluctuations in the base and mixture gas within this value range. This results in the calibration line CL, the dash-dotted diagonal of the figure in Fig. 5 PP 1 is used in the base gas and in the mixing gas. PP 2 measured ( Fig. 3 ), from which the apparent mixture proportions C 2 (PP 1 ) for the base gas and C 2 ( PP 2 ) for the mixing gas. PP mix determined, with which an apparent mixture proportion C 2 ( PP mix ) is issued for the mixing ratio. To determine the effective mixing ratio C 2eff To obtain the amount of the added gas in the mixture, it is best to set up the system of equations for the in Fig. 5 The effective measurement line ML eff is shown as a solid line.

[0035] Equations (6) - (10) remain formally unchanged, except that the slope s of the calibration line is now given by... s : = 100 % PP max − PP min must be set.

[0036] Again, the original system of equations (6) with the measured physical properties of the gases is replaced by the system of equations (9) with the apparent mixing proportions. C 2 (PP 1 ), C 2 (PP 2 ) and C 2 ( PP mix ) has been replaced.

[0037] When determining the mixing ratios, it is advantageous to first convert values ​​of physical properties that are subject to nonlinear mixing rules using a nonlinear function, so that the corresponding function values ​​or sensor signals are subject to linear mixing rules. For physical properties that are subject to nonlinear mixing rules, the Fig. 4 and 5 to be understood in each case with regard to the values ​​converted internally or externally to the sensor (see Fig. 6 ).

[0038] Many sensor types are supplied with an analog 4-20 mA interface. This output signal should then be linearly related to the desired target variable, in this case the mixing ratio or apparent mixing ratio of the admixture gas. Fig. 7 The non-linear mixing rule is shown using the example of the thermal conductivity λ for mixtures of methane and carbon dioxide (biogas), along with its conversion to a linear 4–20 mA output signal from the sensor. The mixing proportions C CH4 are proportional to the sensor output signal after conversion I S .

[0039] If only one measured physical property is available, what has been said applies only to the simultaneous mixing of two gas streams, because with three or more simultaneous input gas streams, a single value for the physical gas property in the output gas stream can be ambiguous. If n gases are mixed together ( Fig. 8 The above can easily be extended to n-1 physical quantities that can be measured with n-1 to (n-1) · (n+1) = n²<-1 sensors. The system of equations (6) is extended to n equations and reads: C 1 eff ⋅ PP 1.1 + C 2 eff ⋅ PP 2.1 + ⋯ + C neff ⋅ PP n .1 = PP mix .1 C 1 eff ⋅ PP 1.2 + C 2 eff ⋅ PP 2.2 + ⋯ + C neff ⋅ PP n .2 = PP mix .2 ⋮ ⋮ C 1 eff ⋅ PP 1 . n − 1 + C 2 eff ⋅ PP 2 . n − 1 + ⋯ + C neff ⋅ PP n . n − 1 = PP mix . n − 1 C 1 eff + C 2 eff + ⋯ + C neff = 1 with the unknown C 1eff until C neff .

[0040] Again, the first n-1 equations can be solved on both sides using the slope. s i = 100% / (PP maxi - PP mini ) the physical property PP i be multiplied by the corresponding calibration curve ( i = 1 up to n - 1), without this having any bearing on the solution of the unknowns C 1eff until C neff changes. Now, analogous to the system of equations (8), the left and right sides of the first n-1 equations are each replaced with the equations that are s i ·PP mini The multiplied left or right side of the last equation is subtracted, resulting in a new system of equations for the unknowns, analogous to equation systems (8) and (9). C 1eff until C neff as a function of the (n-1)·(n+1) = n 2< -1 apparent mixture proportions C 1.1 (PP 1.1 ), C 2.1 (PP 2.1 ) to C n.n- 1 ( PP n.n-1 ) arises: C 1 eff ⋅ C 1.1 PP 1.1 + C 2 eff ⋅ C 2.1 PP 2.1 + ⋯ + C neff ⋅ C n .1 PP n .1 = C mix .1 PP mix .1 C 1 eff ⋅ C 1.2 PP 1.2 + C 2 eff ⋅ C 2.2 PP 2.2 + ⋯ + C neff ⋅ C n .2 PP n .2 = C mix .2 PP mix .2 ⋮ ⋮ C 1 eff ⋅ C 1 . n − 1 PP 1 . n − 1 + C 2 eff ⋅ C 2 . n − 1 PP 2 . n − 1 + ⋯ + C neff ⋅ C n . n − 1 PP n . n − 1 = C mix . n − 1 PP mix . n − 1 C 1 eff + C 2 eff + ⋯ + C neff = 1

[0041] To solve this system of equations, determinants can be used, for example, up to n = 3. From n = 4 onwards, it is recommended to use other numerical methods such as Gaussian elimination.

[0042] If fluctuations in gas composition are only expected in m of the n mixing gases, then consequently only m·(n - 1) sensors are needed to measure the apparent mixing fraction of these m gases. The (n - m)·(n - 1) physical properties PP m+1.1 , PP m+1.2 ... PP n.n -1 of the remaining n - m gases are known from the composition of these gases, from which the apparent mixture proportions can be determined. C m +1.1 (PP m+1.1 ), C m +1.2 ( PP m+1.2 ) ... C n.n -1 (PP n.n-1 ) in the system of equations (12) from the calibration curve for the apparent mixing proportions (dashed-dotted figure diagonal CL in Fig. 5 ) calculate.

[0043] In the method for determining the proportions of gases when mixing n = 2 or 3 or 4 or more gases according to the present invention, n-1 physical properties are measured in the mixed gas and / or in one or more of the n gases, wherein the n-1 physical properties can be measured, for example, with two or three or more sensors, and wherein the proportions of the n gases in the mixed gas are determined from the values ​​of the measured physical property or properties.

[0044] Advantageously, at least one physical property is measured in both the mixed gas and in at least one of the n gases, or at least one or at least two physical properties are measured in the mixed gas.

[0045] In an advantageous embodiment, for those physical properties for which a linear relationship exists between the physical property measured in the mixed gas on the one hand and the corresponding physical property and the mixing proportions of the n gases on the other hand, or for which the deviation from linearity in the area in which measurement is taken lies within a tolerance range of 0.2% or 0.5% or 1%, the corresponding linear relationship is used to determine the mixing proportions.

[0046] For those physical properties for which there is no linear relationship between the physical property measured in the mixed gas on the one hand and the corresponding physical property and the mixing proportions of the n gases on the other hand and / or for which the deviation from linearity in the area in which measurement is taken is outside a tolerance range of 0.2% or 0.If the value of the physical property in question is 5% or 1%, it is advantageous to replace the values ​​of the physical property in question with function values ​​determined by substituting the former into a non-linear function, for example by substituting them into a polynomial of the second, third or higher degree, so that the function value of the physical property measured in the mixed gas depends linearly on the function values ​​of the physical property in question and the mixing proportions of the n gases, and for determining the mixing proportions, the linear relationship between the function value of the physical property measured in the mixed gas and the function values ​​of the corresponding physical property and the mixing proportions of the n gases is used in each case.

[0047] In a further advantageous embodiment, for those physical properties for which a linear relationship is used between the physical property measured in the mixed gas on the one hand and the corresponding physical property and the mixture proportions of the n gases on the other hand, the physical property measured in the mixed gas is considered a linear combination of the corresponding physical property of the n gases, and for those physical properties for which no linear relationship is used between the physical property measured in the mixed gas on the one hand and the corresponding physical property and the mixture proportions of the n gases on the other hand, the function value determined from the value of the physical property measured in the mixed gas is considered a linear combination of the function values ​​determined from the values ​​of the corresponding physical property of the n gases.Advantageously, for all n-1 physical properties, the mixing proportions correspond to the coefficients of the linear combinations, and the mixing proportions can be determined from the n-1 linear combinations and from the knowledge that the sum of the mixing proportions is equal to one or 100%.

[0048] Typically, for those of the n gases in which none or not all of the n - 1 physical properties are measured, predetermined values ​​are used to determine the proportions of the mixture for the unmeasured physical properties or for the function values ​​determined from them, whereby the predetermined values ​​can be determined, for example, from the composition of the gases in question.

[0049] Physical properties such as thermal conductivity, heat capacity, density, viscosity, speed of sound, diffusion coefficient, refractive index, dielectric constant and / or optical absorption coefficient at a specific wavelength of electromagnetic radiation can be measured.

[0050] In a preferred embodiment, the n - 1 physical properties in the mixed gas are measured with sensors, each of which contains a calibration curve for the respective physical property for determining an apparent mixing ratio, i.e., a mixing ratio for a gas composition that does not need to correspond to the actual gas composition present, and from the apparent mixing ratios determined in this way for each of the n gases, the effective mixing ratio in the mixed gas is determined.

[0051] If required, the n - 1 physical properties in one or more of the n gases can be measured with sensors, each containing a calibration curve for the relevant physical property for determining an apparent mixing ratio, which is identical to the calibration curve in the sensor used for measuring the relevant physical property in the mixed gas, and from the apparent mixing ratios thus determined for each of the n gases the effective mixing ratio in the mixed gas is determined.

[0052] Advantageously, for those of the n gases in which none or not all of the n-1 physical properties are measured, predetermined values ​​are used for the apparent mixture proportions, whereby the predetermined values ​​are determined, for example, from the composition of the gases in question.

[0053] In an advantageous embodiment, values ​​of physical properties that are subject to nonlinear mixing rules are first converted using a nonlinear function, so that the function values ​​or corresponding sensor signals are subject to linear mixing rules.

[0054] A physical property PP i is subject to a linear mixing rule if PP mix . i = C 1 ⋅ PP 1 . i + C 2 ⋅ PP 2 . i + ⋯ + C n ⋅ PP n . i , where PP mix.i and PP 1, i ... PP n,i the physical property in the mixed gas and in the n gases and C 1 ... C n correspond to the mixture proportions of the n gases.

[0055] On the other hand, this means that a physical property PP i is subject to a non-linear mixing rule if PP mix . i ≠ C 1 ⋅ PP 1 . i + C 2 ⋅ PP 2 . i + ⋯ + C n ⋅ PP n . i .

[0056] In an advantageous embodiment, n ≥ 3 gases are mixed sequentially by first mixing two gases, then mixing the mixed gas with another gas in a further two-gas mixing process, and repeating the mixing of the last mixed gas with another gas until all n gases are mixed together, wherein all sensors are identically calibrated for the same physical property.

[0057] In another advantageous embodiment, n ≥ 4 gases are mixed in pairs in a first cascade, and then the respective mixed gases are mixed in pairs in one or more further cascades until all n gases are mixed, with all sensors being identically calibrated for the same physical property.

[0058] In another advantageous embodiment, the mixing of the n ≥ 4 gases takes place in a combination of sequential and cascaded mixing, with all sensors being identically calibrated for the same physical property.

[0059] The invention further comprises a measuring device for determining the mixing proportions when mixing n = 2, 3, 4 or more gases, which includes one or more sensors for measuring n-1 physical properties in the mixed gas and / or in one or more of the n gases and an evaluation unit connected to the sensors, and which is configured to carry out a method according to the present invention or one of the embodiments or variants described above.

[0060] The evaluation unit can, for example, be designed in or integrated into a computing or control unit of a mixing device. Furthermore, the measuring device and / or one or more of the sensors can be designed as portable devices.

[0061] In a further advantageous embodiment of the method for determining the proportion of mixtures when mixing n = 2, 3, 4 and more gases according to the present invention, physical properties in the mixed gas are measured with one or more sensors n-1, wherein a corresponding calibration curve for determining an apparent concentration is stored for each physical property, e.g. in the corresponding sensor(s), and apparent concentrations are calculated from the measured values ​​for the n-1 physical properties using the respective calibration curve, and the effective concentrations of the n gases in the mixed gas are determined from the apparent concentrations.

[0062] If necessary, the physical properties of n - 1 of the gases to be mixed can also be measured in 1 ≤ m ≤ n, whereby apparent concentrations are determined for each of the m gases to be mixed from the measured values ​​for the n - 1 physical properties using the respective calibration curve, and the effective concentrations of the n gases in the mixed gas are determined from the apparent concentrations of the m gases to be mixed and those of the mixed gas.

[0063] In an advantageous embodiment where n = 2 and m = 0, the known physical property PP 1 and PP 2. The apparent mixing proportions of gases 1 and 2 were calculated and combined with the information obtained from the measured physical property. PP mix The effective concentration of gas 2 is determined by the apparent proportion of the mixed gas, and the effective concentration of gas 1 in the mixed gas is determined by its complement to 100%.

[0064] In another advantageous embodiment, where n = 2 and m = 1, the known physical property PP 2 of gas 2, the apparent mixture fraction of gas 2 is calculated and together with the measured physical properties PP 1 and PP mix The effective concentration of gas 2 is determined by certain apparent proportions of gas 1 and the mixed gas, and in its complement to 100%, the effective concentration of gas 1 in the mixed gas is determined.

[0065] In another advantageous embodiment, where n = 2 and m = 2, the physical properties obtained from the measured parameters are used. PP 1 , PP 2 and PP mix The effective concentration of gas 2 is determined from certain apparent proportions of gas 1, gas 2 and the mixed gas, and the effective concentration of gas 1 in the mixed gas is determined in its complement to 100%.

[0066] The physical properties can include, for example, thermal conductivity, heat capacity, density, viscosity, speed of sound, diffusion coefficient, refractive index, dielectric constant and / or optical absorption coefficient at a specific wavelength of electromagnetic radiation.

[0067] If the physical property is thermal conductivity, the sensor(s) are advantageously calibrated for the range of values ​​from krypton (λ=9.5·10 -3< W m -1< K -1< at 25 °C and 1013 mbar) to hydrogen (λ = 0.186 W m -1< K -1< at 25 °C and 1013 mbar).

[0068] Advantageously, physical properties that are subject to nonlinear mixing rules are first converted to a linear sensor signal according to this nonlinear mixing rule, for example using a nonlinear function, so that the function values ​​or corresponding sensor signals are subject to linear mixing rules.

[0069] In an advantageous embodiment, two gases are first mixed sequentially, and then the mixed gas is mixed with a third gas in a further two-gas mixing process, and this mixed gas is then mixed with a fourth gas, until n ≥ 3 gases are mixed together.

[0070] In another advantageous embodiment, 4, 8 or 12 of the n ≥ 4 gases are mixed in a first cascade, and then the respective mixed gases are mixed in pairs in a second cascade until all n gases are mixed.

[0071] In another advantageous embodiment, the mixing of the n ≥4 gases takes place in a combination of sequential and cascaded mixing.

[0072] The invention further comprises a mixing device comprising a gas mixing unit with at least two gas supply lines and a gas outlet line, as well as an evaluation unit, wherein sensors for n-1 physical properties are arranged in the gas outlet line and, if required, in one or more gas supply lines, and wherein the sensors are connected to the evaluation unit, which is configured to carry out a method according to the present invention or one of the embodiments or variants described above.

[0073] In an advantageous embodiment, the evaluation unit is formed in a computing or control unit of the mixing device.

[0074] Advantageously, the sensor or sensors for a specific physical property are identically calibrated to a measuring range that is larger than the expected range of values ​​for this physical property of the n gases.

[0075] In a preferred embodiment of the mixing device for mixing n ≥ 3 gases, the mixing device comprises n - 1 sequentially arranged gas mixing units, each with two gas supply lines and one gas outlet line, wherein the gas outlet line of a gas mixing unit, with the exception of the gas outlet line of the last gas mixing unit, is connected to a gas supply line of the subsequent gas mixing unit.

[0076] In a further preferred embodiment of the mixing device for mixing 2 n< gases, where n ≥ 2, the mixing device 2 n< -1 comprises gas mixing units arranged in a binary tree structure, each with two gas supply lines and one gas outlet line.

[0077] Most known methods for determining the proportions of gas mixtures using sensors that measure one or more physical properties of the gas mixture assume that the incoming gas flows are known and remain constant in composition throughout the mixing process. In contrast to the method and mixing device according to the present invention, the sensors are individually calibrated differently for each mixing process and deliver incorrect results if the composition of one of the gases being mixed changes. The method and mixing device according to the present invention, however, have the advantage of enabling the correct determination of the proportions even if the composition of the gases being mixed changes.

[0078] The method and measuring device according to the present invention have an advantage over the method described in WO 02 / 40992 A1 for determining the mixture proportions of a four-component gas mixture in that, in the method according to the invention, physical properties that are subject to nonlinear mixing rules are first converted so that the converted values ​​are subject to linear mixing rules. This makes it possible to determine the mixture proportions more accurately. In contrast, the method from WO 02 / 40992 assumes that the three physical quantities being measured depend linearly on the mixture proportions, which is not the case, for example, for thermal conductivity.

[0079] The linear system of equations for determining the mixture proportions in WO 02 / 40992 A1, page 5, contains twelve constants that must be determined from known values ​​of the measured quantities using regression analysis. In contrast, the inventive method has the advantage that the systems of equations (5) and (12) for determining the mixture proportions contain exclusively constants that are given by the actual measurement of the physical properties or are known from literature or databases. Therefore, unlike the prior art, no additional calibration is required to determine the constants.

[0080] The invention will be explained in more detail below with reference to the drawings. The drawings show: Fig. 1 shows an example of the mixing of two gases, where the physical property is only present in the mixed gas. PP mix is measured (n = 2, m = 0), Fig. 2 a second example of the mixing of two gases, where the physical property is in the base gas and in the mixed gas PP 1 and PP mix measured (n = 2, m = 1), Fig. 3 a third example of mixing two gases, wherein the physical property is present in the base gas, in the admixture gas and in the mixed gas. PP 1 , PP 2 and PP mix are measured (n=2, m=2), Fig. 4 is an example of a calibration and measurement curve of the physical property PP when mixing a base gas G1 with the mixing gas G2 in the case of fluctuations in the physical property PP 1 in the base gas (n = 2, m = 1), Fig. 5 a second example of a calibration and measurement curve of the physical property PP when mixing a base gas G1 with the mixing gas G2 in the case of fluctuations in the physical property PP 1 in the ground gas and PP 2 in the mixing gas (n=2, m=2), Fig. 6 an example of a conversion of the sensor signal to a linear characteristic curve in the case of non-linear mixing behavior of the physical property PP Fig. 7 shows an example of converting the sensor signal to a linear characteristic curve with respect to the mixing ratio in the case of nonlinear mixing behavior for the physical property "thermal conductivity" for methane / carbon dioxide mixtures; Fig. 8 shows an example of the simultaneous mixing of n gases with sensors for n - 1 physical properties PP i , ( i = 1, ... , n - 1), Fig. 9 an example of the sequential mixing of n gases with sensors for a physical property PP Fig. 10 shows an example of the cascaded mixing of 2 n< gases with sensors for a physical property PP , and Fig. 11 shows an example of a mixing device for mixing two gases together with an embodiment of a measuring device according to the present invention.

[0081] The Figuren 1, 2 und 3 Examples show the mixing of two gases G1 and G2, which are fed into a gas mixing unit 4. The physical property of the mixed gas Gmix is ​​measured using a sensor 3. PP mix measured. In the Fig. 1 In the example shown, the determination of the mixture proportions is based on the assumption that the composition of gases G1 and G2 is known.

[0082] If only the composition of the mixing gas G2 is known, while the composition of the base gas G1 is subject to fluctuations, the physical property is determined in the method according to the present invention. PP 1 additionally, as in Fig. 2 shown, also measured in the ground gas with a sensor 3.1.

[0083] In the Fig. 3 In the example shown, the determination of the mixing proportions is based on the assumption that the compositions of the base gas G1 and the mixing gas G2 are subject to fluctuations. In this case, the physical property PP 1 , PP 2 additionally measured with one sensor each 3.1 and 3.2 in both the base gas and the mixed gas.

[0084] In a first embodiment of the method according to the present invention, the determination of the mixture proportions is shown using the example of biogas conditioning. During conditioning, methane from biogas production is mixed with CO₂ and propane.

[0085] To determine the proportions of the mixture, the density and viscosity of the mixed gas are measured. The values ​​for methane, CO₂, and propane are not measured but assumed to be known. Gas / physikalische Eigenschaft 25 °C, 1013.25 mbar Methan CO 2 Propan Messung konditioniertes Biomethan Dichte [kg / m 3< ] 0.657 1.808 1.832 0.876 Viskosität [µPa·s] 11.1 14.9 8.12 11.2

[0086] Substituting the density and viscosity into the system of equations (5) yields: C 1 ⋅ ρ 1 + C 2 ⋅ ρ 2 + C 3 ⋅ ρ 3 = ρ mix C 1 ⋅ η 1 + C 2 ⋅ η 2 + C 3 ⋅ η 3 = η mix C 1 + C 2 + C 3 = 1 or, if the mixture proportions are expressed in mol%, C 1 ⋅ ρ 1 + C 2 ⋅ ρ 2 + C 3 ⋅ ρ 3 = ρ mix ⋅ 100 mol% C 1 ⋅ η 1 + C 2 ⋅ η 2 + C 3 ⋅ η 3 = η mix ⋅ 100 mol% C 1 + C 2 + C 3 = 100 mol%

[0087] Using the values ​​from the example and by omitting the units of measurement, one obtains C 1 ⋅ 0.657 + C 2 ⋅ 1.808 + C 3 ⋅ 1.832 = 0.876 ⋅ 100 mol% C 1 ⋅ 11.1 + C 2 ⋅ 14.9 + C 3 ⋅ 8.12 = 11.2 ⋅ 100 mol% C 1 + C 2 + C 3 = 100 mol%

[0088] The solution to the above system of equations can be found, for example, using Cramer's rule (determinant method). The solution is obtained as follows: C 1 = 81.1 mol% (methane), C 2 = 9.8 mol% (CO 2 ) and C 3 = 9.1 mol% (propane). The measured values ​​actually come from a conditioned biomethane with the composition C1 = 81 mol%, C2 = 10 mol% and C3 = 9 mol%.

[0089] A second embodiment of the method according to the present invention is described below using the example of adding hydrogen to natural gas pipelines. Since the composition of natural gas can change constantly, for example because the natural gas originates from different sources depending on availability and price, it is advantageous to measure both the natural gas before and the mixed gas after the addition of hydrogen in order to determine the amount of hydrogen added. Since the properties of pure hydrogen are known, no additional sensor is needed for the latter.

[0090] In the second embodiment, the thermal conductivity λ is measured as a physical property, requiring two sensors whose measuring range covers thermal conductivities from λ = 25.84 mW / m < K⁻¹ (nitrogen, N₂) to λ = 185.8 mW / m < K⁻¹ (hydrogen, H₂). Nitrogen corresponds to a measured hydrogen concentration of 0 mol%, while pure hydrogen represents 100 mol%. However, the thermal conductivity of a mixture of H₂ and N₂ is not proportional to the molar concentration of H₂ in N₂. Thus, a 50% / 50% mixture has a linearly calculated thermal conductivity of 105.8 mW / m < K⁻¹, while the actual value is 76.42 mW / m < K⁻¹. If the latter were substituted into the system of equations (6) and the corresponding solution, equation (10), a mixture of 68.4% / 31.6% N 2 / H 2 would result.Consequently, the sensor output signal must be converted to a linear mixing rule due to the nonlinear mixing rule. The sensor output signal is, for example, supplied by an analog 4-20 mA current output, as is found in many sensors. The conversion to a linear mixing rule can be performed using a polynomial, specifically y = -3.00E-13·x 6< + 2.40E-10-x 5< - 8.43E-08·x 4< + 1.78E-05·x 3< - 2.66E-03·x 2< + 3.24E-01 x - 2.86, where y is the current output signal. I S and x represents the thermal conductivity. PP min = 4 mA then corresponds to pure N2. PP max = 20 mA of pure H₂. Substituting the measured mixed value of 76.42 mW m⁻¹ < K⁻¹ < for a 50% / 50% mixture yields a current of 12.0 mA.

[0091] These three current values ​​can be substituted into the system of equations (6). For the slope of the calibration curve CL in Fig. 4 follows = (100% - 0%) / (20 mA - 4 mA) = 6.25 % / mA). Substituting into equation (8), C 1 eff + C 2 eff = 1 and further in equation (9) C 1 eff ⋅ 0 % + C 2 eff ⋅ 100 % = 50 % C 1 eff + C 2 eff = 1 This leads to effective concentrations of 50 mol% each for N2 and H2.

[0092] In the second embodiment, if the natural gas originates from two different sources, with the natural gas from the first source having a thermal conductivity of 31.66 mW / (m⁻¹ < K⁻¹) and that from the second source having a thermal conductivity of 33.69 mW / (m⁻¹ < K⁻¹), the sensor will linearize and measure 5.22 mA and 5.62 mA, respectively, which corresponds to a hydrogen concentration of (5.22 mA - 4 mA) / (20 mA - 4 mA) = 7.63% and 10.13% H₂ in N₂, respectively. However, neither of the natural gases naturally contains hydrogen. Now, the measured value in the mixed gas must be converted to a linear mixing rule: this is 82.19 mW m⁻¹ < K⁻¹ < for natural gas from the first source and 85.29 mW m⁻¹ < K⁻¹ < for natural gas from the second source, again with an admixture of 50 mol% H₂, which results in a sensor signal of 12.64 mA and 12.97 mA, respectively. Or, expressed as H₂ concentration: 54.07% and 56.14%, respectively. These are the values ​​to be inserted into the system of equations (9).The solution, equation (10), is for the natural gas from the first source . C H2eff = (54.00%-7.63%) / (100%-7.63%) = 50.20% and C H2eff = (56.06% - 10.13%) / (100% - 10.13%) = 51.11% for the natural gas from the second source. Without converting the thermal conductivity values ​​to a linear mixing rule, the H₂ concentration would have been 32.8% for the natural gas from the first source and 33.9% for the natural gas from the second source, which is significantly inaccurate compared to the actual admixture of 50 mol% H₂. All gas properties in this example are given for 25°C and 1013.25 mbar.

[0093] In a third embodiment, the conditioning of biomethane is described in more detail. Propane and / or air are added to the biomethane to condition the calorific value and / or the Wobbe index in the downstream natural gas network to a locally typical value. Since the composition of the biomethane can change, for example, because it depends on the biomass fed into the digester of the biogas plant, it is advantageous to measure both the biomethane before and the mixed gas after the addition of propane / air in order to determine the amount of the latter added. Because the properties of pure propane and pure air are known, no additional sensor is needed for these gases: This example therefore represents the case n = 3, m = 1. Let the density ρ and the thermal conductivity λ be the physical properties that are measured with two corresponding sensors, whose measuring ranges densities from ρ = 0.657 kg / m 3< (methane, CH 4 ) to ρ =1.832 kg / m 3< (propane) and thermal conductivities from λ = 18.31 mW m -1< K -1< (propane) to λ = 33.96 mW m -1< K -1< (methane, CH 4 ).

[0094] While density is calculated using a linear mixing rule, meaning the gases to be mixed are considered ideal (the deviation from real gases in this example is only 0.2% in density), thermal conductivity is subject to a nonlinear mixing rule. Therefore, in this example as well, the sensor output signal must be converted to a linear mixing rule. This sensor output signal is supplied, for example, by an analog 4-20 mA current output, as found in many sensors. Since the thermal conductivity range is somewhat narrower than in the hydrogen mixing example above, a third-order polynomial suffices here: y = 1.75E-03·x 3< - 1.78E-01·x 2< + 6.63·x - 68.46, where y is the current signal. I Sand x represents the thermal conductivity. In the example, two biomethane mixtures are to be conditioned to achieve a calorific value of 33.6 MJ / m³ and a Wobbe index of 40.3 MJ / m³. Table 1 Conditioning of biomethane 1 Abbreviations: WLF = Thermal conductivity The values ​​for air and propane are not measured, but assumed to be known. Gas / physical property Biomethane composition 1 Air propane conditioned biomethane 1 CH 4 92% 79.02% H 2 0% 0% N 2 4% 3.44% CO2 4% 3.44% Addition: propane 0% 5.10% Air 0% 9.00% Calorific value [MJ / m³] 33.55 0 92.20 33.52 Wobbe index [ MJ / m³< ] 42.96 0 74.13 40.30 Density [kg / m³<] 0.722 1.184 1.832 0.819 Signal [mA] 4.90 11.18 20.00 6.22 s·(PP- PP min ) s=100% / (I s -4mA) 6.25% / mA· (4.90 - 4)mA = 5.62% 6.25% / mA· (11.18-4)mA = 44.87% 6.25% / mA · (20.00-4)mA = 100% 6.25% / mA (6.22 - 4)mA = 13.87% WLF [mWm -1< K -1< ] 32.90 26.25 18.31 30.98 Signal [mA] 19.32 14.58 4.00 18.13 s· ( PP- PP min ) s=100% / (I s -4mA) 6.25% / mA (19.32 - 4)mA = 95.75% 6.25% / mA· (14.58-4)mA = 66.12% 6.25% / mA · (4.00-4)mA = 0% 6.25% / mA (18.13 - 4)mA = 88.31%

[0095] The system of equations (12) now reads: C 1 eff ⋅ 5.62 % + C 2 eff ⋅ 44.87 % + C 3 eff ⋅ 100 % = 13.87 % C 1 eff ⋅ 95.75 % + C 2 eff ⋅ 66.12 % + C 3 eff ⋅ 0 % = 88.31 % C 1 eff + C 2 eff + C 3 eff = 100 %

[0096] The solution to this system of equations is obtained C 1eff = 85.9% Biomethane 1, C 2eff = 9.12% air and C 3eff = 4.95% propane, resulting in a calorific value of 33.39 MJ / m³ and a Wobbe index of 40.25 MJ / m³. Compared to the (actual) values ​​in Table 1: 85.9% biomethane, 9.00% air, and 5.1% propane. Table 2 Conditioning of biomethane 2 Abbreviations: WLF = Thermal conductivity The values ​​for air and propane are not measured, but assumed to be known. Gas / physical property Biomethane composition 2 Air propane conditioned biomethane 2 CH 4 94% 72.48% H 2 4% 3.08% N 2 0% 0% CO2 2% 1.54% Addition: propane 0% 7.40% Air 0% 15.50% Calorific value [MJ / m³] 34.74 0 92.20 33.61 Wobbe index [ MJ / m³< ] 46.65 0 74.13 40.30 Density [kg / m³<] 0.657 1.184 1.832 0.824 Signal [mA] 4.00 11.18 20.00 6.27 s· ( PP-PP min ) s=100% / (I s -4mA) 6.25% / mA· (4.00 - 4)mA = 0% 6.25% / mA· (11.18-4)mA = 44.87% 6.25% / mA · (20.00 - 4)mA = 100% 6.25% / mA· (6.27 - 4)mA = 14.19% WLF [mWm -1< K -1< ] 36.68 26.25 18.31 32.77 Signal [mA] 21.60 14.58 4.00 19.24 s·(PP- PP min ) s=100% / (I s -4mA) 6.25% / mA· (21.60 - 4)mA = 110.0% 6.25% / mA· (14.58-4)mA = 66.12% 6.25% / mA· (4.00 - 4)mA = 0% 6.25% / mA. (19.24 - 4)mA = 95.25%

[0097] The system of equations (12) now reads: C 1 eff ⋅ 0 % + C 2 eff ⋅ 44.87 % + C 3 eff ⋅ 100 % = 14.19 % C 1 eff ⋅ 110.0 % + C 2 eff ⋅ 66.12 % + C 3 eff ⋅ 0 % = 95.25 % C 1 eff + C 2 eff + C 3 eff = 100 %

[0098] The solution to this system of equations is obtained C 1eff = 77.16% Biomethane 2, C 2eff = 15.68% air and C 3eff= 7.16% propane, resulting in a calorific value of 33.40 MJ / m³ and a Wobbe index of 40.22 MJ / m³. Compared to the (actual) values ​​in Table 2: 77.1% biomethane 2, 15.5% air, and 7.4% propane. Biomethane 2 has a thermal conductivity outside the 4–20 mA range, leading to concentration values ​​exceeding 100%. In practice, a thermal conductivity sensor with a larger measuring range than used in this example would be required. However, it is interesting to see that the underlying calculation principle yields the correct effective concentrations even with non-physical values. All gas properties in this example are given for 25 °C and 101 3.25 mbar.

[0099] Fig. 8 Figure 1 shows an embodiment for the simultaneous mixing of n gases G1, ..., Gn, which are supplied to a gas mixing unit 4. In the method according to the present invention, n - 1 sensors 3.1,..., are placed in the mixed gas Gmix 1...n. n-1n - 1 physical properties PP mix,1 , ..., PP mix.n-1 measured. In the illustrated version, it is assumed that the composition of the gases to be mixed G1, ..., Gn is subject to fluctuations, which is why the n - 1 physical properties PP 1.1 , ... , PP no -1 with n·(n-1) sensors 3.1. 1,..., n - 1, ..., 3.n.1,..., n-1 They can also be measured in the gases to be mixed.

[0100] If, as in the example of the in Fig. 9In the illustrated implementation variant, where the gases are mixed sequentially, the mixing of n incoming gas flows can also be monitored using only one physical gas property: Gas G1 is first mixed with Gas G2, this mixture then with Gas G3, and so on, until all n gases are mixed. This requires n - 1 gas mixing units 4.1, ..., 4.n-1 and a maximum of 2n - 1 sensors, because each sensor 3.12 ... 3.1-n is located after one of the first n - 2 mixing stages and gas mixing units 4.1 ... 4.n-2 in Fig. 9 It also serves as a sensor for one of the gases in the next mixing stage. If the mixing gas in one of the mixing stages is known in advance, no additional sensor is needed (see below). Fig. 2 The minimum number of sensors is n-1 if all mixing gases are known.

[0101] Fig. 10Figure 1 shows one implementation variant of cascaded mixing: The n gases are mixed in pairs in a first stage, these mixtures are then mixed again in pairs in a second stage, until finally all gases are mixed. Again, a maximum of 2n - 1 and a minimum of n - 1 sensors are required. This is supplemented by n - 1 gas mixing units.

[0102] Further design variants result from the combination of sequential and cascaded mixing and / or by, for example, mixing three gases in each stage during sequential mixing, in which case sensors for two physical properties must be provided in each case.

[0103] Fig. 11Figure 9a or 9b shows an example of a mixing device for mixing two gases 1.1 and 1.2 together with an embodiment of a measuring device for determining the mixing proportions according to the present invention. The mixing device 9a or 9b comprises a gas mixing unit 4, two gas inlets 5.1 and 5.2 for supplying the gases 1.1 and 1.2 to be mixed, and a gas outlet line 6 for the mixed gas 2.

[0104] The measuring device of the exemplary embodiment comprises a sensor 3.1, 3.2 for measuring a physical property of the two supplied gases 1.1 and 1.2, a third sensor 3 for measuring the same physical property in the mixed gas and an evaluation unit 8, which is connected to the three sensors and is configured to carry out a method according to the present invention or one of the embodiments or variants described above.

[0105] The sensors 3.1 and 3.2 for the gases to be mixed can, for example, be arranged in the gas inlets 5.1 and 5.2, and the third sensor 3 for the mixed gas in the gas outlet line 6. The evaluation unit 8 can optionally be designed separately or in a computing or control unit of the mixing device 9a.

[0106] If the physical property can be calibrated over a wide range of values ​​without loss of accuracy, the sensors can be used universally: The calibration curve for the apparent mixing ratio then covers a very large range of possible gas compositions. This reduces production and storage costs, as only one sensor type per physical property needs to be manufactured and stored. For example, sensors designed for quality assurance of biogas (a mixture of carbon dioxide, CO₂, and methane, CH₄) can also be used for mixing nitrox breathing gas mixtures for divers (a mixture of nitrogen, N₂, and oxygen, O₂) if the physical property is either density or thermal conductivity.

Claims

1. Method for determining the mixing proportions when mixing n = 2, 3, 4 or more gases, in which at least n - 1 physical properties are measured in each case in the mixed gas and in one or more of the n gases, wherein • the n - 1 physical properties are measured using at least two sensors, and • the mixing proportions of the n gases in the mixed gas are determined from the values of the measured physical property or properties, characterized in that the n - 1 physical properties in the mixed gas are measured using sensors on which a calibration curve for determining an apparent mixing proportion, i.e. a mixing proportion for a gas composition which does not need to correspond to the effectively present gas composition, is stored in each case for the relevant physical property, and the n - 1 physical properties in one or more of the n gases are measured using sensors on which a calibration curve for determining an apparent mixing proportion is stored in each case for the relevant physical property, wherein said calibration curve is identical to the calibration curve in the sensor used for measuring the relevant physical property in the mixed gas, and the effective mixing proportion in the mixed gas is determined from the apparent mixing proportions determined in this way for each of the n gases.

2. Method according to claim 1, in which at least one physical property is measured both in the mixed gas and in at least one of the n gases or at least two physical properties are measured in the mixed gas.

3. Method according to claim 1 or 2, in which, for those physical properties for which there is a linear relationship between the physical property measured in the mixed gas, on the one hand, and the corresponding physical property and the mixing proportions of the n gases, on the other hand, or for which the deviation from the linearity in the range in which measurement is carried out lies within a tolerance range of 0.2% or 0.5% or 1%, the corresponding linear relationship is used for determining the mixing proportions.

4. Method according to any one of claims 1 to 3, in which, for those physical properties for which there is no linear relationship between the physical property measured in the mixed gas, on the one hand, and the corresponding physical property and the mixing proportions of the n gases, on the other hand, and for which the deviation from the linearity in the range in which measurement is carried out lies outside a tolerance range of 0.2% or 0.5% or 1%, the values of the relevant physical property are replaced by functional values which are determined by inserting the former into a nonlinear function, for example by inserting into a polynomial of the second, third or higher degree, such that the functional value of the physical property measured in the mixed gas depends linearly on the functional values of the relevant physical property and the mixing proportions of the n gases, and the linear relationship between the functional value of the physical property measured in the mixed gas and the functional values of the corresponding physical property and the mixing proportions of the n gases is used in each case for determining the mixing proportions.

5. Method according to any one of claims 1 to 4, in which, for those physical properties for which a linear relationship between the physical property measured in the mixed gas, on the one hand, and the corresponding physical property and the mixing proportions of the n gases, on the other hand, is used, the physical property measured in the mixed gas is considered as a linear combination of the corresponding physical property of the n gases, and, for those physical properties for which no linear relationship between the physical property measured in the mixed gas, on the one hand, and the corresponding physical property and the mixing proportions of the n gases, on the other hand, is used, the functional value which is determined from the value of the physical property measured in the mixed gas is considered as a linear combination of the functional values determined from the values of the corresponding physical property of the n gases, wherein, for all n - 1 physical properties, the mixing proportions correspond to the coefficients of the linear combinations, and the mixing proportions are determined from the n - 1 linear combinations and from the knowledge that the sum of the mixing proportions is equal to one or 100%.

6. Method according to any one of claims 1 to 5, in which, for those of the n gases in which no or not all of the n - 1 physical properties are measured, predetermined values are used in the determination of the mixing proportions for the non-measured physical properties or for the functional values determined from the same, wherein the predetermined values are determined, for example, from the composition of the relevant gases.

7. Method according to any one of claims 1 to 6, wherein the physical property or properties measured are the thermal conductivity, the heat capacity, the density, the viscosity, the speed of sound, the diffusion coefficient, the refractive index, the dielectric constant and / or the optical absorption coefficient at a particular wavelength of electromagnetic radiation.

8. Method according to any one of claims 1 to 7, in which, for those of the n gases in which no or not all of the n - 1 physical properties are measured, predetermined values are used for the apparent mixing proportions, wherein the predetermined values are determined, for example, from the composition of the relevant gases.

9. Method according to any one of claims 1 to 8, wherein values of physical properties which are subject to nonlinear mixing rules are first converted with the aid of a nonlinear function, such that the functional values or corresponding sensor signals are subject to linear mixing rules.

10. Method according to any one of claims 1 to 9, wherein n ≥ 3 gases are mixed sequentially by first mixing two gases and then mixing the mixed gas with a further gas in a further two-gas mixing process and repeating the mixing of the last-mixed mixed gas with a further gas until all n gases are mixed with one another, and wherein all sensors are calibrated identically for the same physical property.

11. Method according to any one of claims 1 to 9, wherein n ≥ 4 gases are respectively mixed into two in a first cascade and then the respective mixed gases are mixed into two in one or more further cascades until all n gases are mixed, and wherein all sensors are calibrated identically for the same physical property.

12. Method according to any one of claims 1 to 9, wherein the mixing of the n ≥ 4 gases is effected in a combination of sequential and cascaded mixing, and all sensors are calibrated identically for the same physical property.

13. Measuring device for determining the mixing proportions when mixing n = 2, 3, 4 or more gases, comprising sensors for measuring n - 1 physical properties in the mixed gas and in one or more of the n gases and an evaluation unit which is connected to the sensors and which is set up to carry out a method according to any one of claims 1 to 12.

14. Measuring device according to claim 13, wherein the evaluation unit is realized in a computing unit or control unit of a mixing device, or wherein the measuring device and / or one or more of the sensors are designed as mobile appliances.