Gas impurity concentration in-situ detection method based on refractive index gas temperature measurement method

Abstract

The invention relates to the technical field of low-temperature metering and gas analysis, and provides a gas impurity concentration in-situ detection method based on a refractive index gas temperature measurement method, which comprises the following steps: measuring the experimental refractive index of mixed gas in a known thermodynamic state; constructing a multi-component mixed gas Virie coefficient model containing cross interaction terms; calculating the theoretical refractive index of the mixed gas based on the Virie coefficient model; a nonlinear optimization algorithm is used for minimizing the residual error of the theoretical refractive index and the experimental refractive index, the mole fraction of each component is solved, and in-situ detection of the gas impurity concentration is achieved; according to the method, in-situ and high-precision detection of the concentration of the gas impurities is realized through an innovative method based on refractive index measurement and a Virie coefficient model, and the method can accurately represent interaction among gas molecules, so that the detection precision is improved, and the method is particularly suitable for analysis of trace impurities.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of cryogenic metrology and gas analysis technology, and particularly relates to a gas impurity concentration in-situ detection method based on a refractive index gas temperature measurement method. BACKGROUND

[0002] In the fields of low-temperature physics, primary temperature measurement, and quantum standard reproduction, the purity of high-purity working gas (such as helium-4, helium-3, neon, etc.) is crucial to the accuracy of experimental results. The traditional refractive index gas temperature measurement method (RIGT) is a primary temperature measurement method based on quantum standards (Boltzmann constant ). The core principle is to detect the thermodynamic temperature by measuring the refractive index and pressure of the gas, combined with the virial coefficient of the gas.

[0003] However, in practical applications, the working gas inevitably contains trace impurities (such as He-3 in He-4 or He in Ne). Existing gas analysis methods (such as gas chromatography-mass spectrometry GC-MS) usually require gas samples to be extracted for offline analysis, which is not only cumbersome to operate, but also difficult to reflect the real state of the gas inside the low-temperature cavity in real time.

[0004] Current RIGT research mainly focuses on evaluating the error caused by impurities on temperature measurement under the condition of known impurity concentration. The existing technical solutions have not yet calculated the composition and proportion of unknown impurities in the gas by the abnormal refractive index measured by the RIGT system. SUMMARY

[0005] The present application provides a gas impurity concentration in-situ detection method based on a refractive index gas temperature measurement method, to solve the problem that the existing low-temperature gas impurity detection method cannot be in-situ, high-precision, and real-time analyzed.

[0006] The present application provides a gas impurity concentration in-situ detection method based on a refractive index gas temperature measurement method, comprising the following steps: Under the known thermodynamic state, the experimental refractive index of the mixed gas is measured; A multi-component mixed gas virial coefficient model containing cross-interaction terms is constructed; The theoretical refractive index of the mixed gas is calculated based on the virial coefficient model; The residual error between the theoretical refractive index and the experimental refractive index is minimized using a nonlinear optimization algorithm, and the molar fraction of each component is solved to realize in-situ detection of the gas impurity concentration.

[0007] The application provides a gas impurity concentration in-situ detection method based on a refractive index gas temperature measurement method.

[0008] The application provides the gas impurity concentration in-situ detection method based on the refractive index gas temperature measurement method, wherein the number of the thermodynamic state points is one or more; when detecting a single impurity, one thermodynamic state point is selected; and when detecting multiple impurities, multiple thermodynamic state points covering different temperature intervals are selected.

[0009] The application provides the gas impurity concentration in-situ detection method based on the refractive index gas temperature measurement method, wherein the multi-component mixed gas virial coefficient model comprises a mixed magnetic virial coefficient and a first dielectric virial coefficient, and both of them adopt a linear mixing rule.

[0010] The application provides the gas impurity concentration in-situ detection method based on the refractive index gas temperature measurement method, wherein the multi-component mixed gas virial coefficient model comprises a high-order dielectric virial coefficient, a second density virial coefficient, a third density virial coefficient and a fourth density virial coefficient, which respectively represent dielectric high-order interaction and two-body, three-body and four-body molecular interaction.

[0011] The application provides the gas impurity concentration in-situ detection method based on the refractive index gas temperature measurement method, wherein the cross interaction term comprises a two-body cross virial coefficient, a three-body cross virial coefficient and a four-body cross virial coefficient, which respectively represent two-body, three-body and four-body interaction between different molecules.

[0012] The application provides the gas impurity concentration in-situ detection method based on the refractive index gas temperature measurement method, wherein the nonlinear optimization algorithm is a Levenberg-Marquardt algorithm or a simplex method, the residual is calculated through a least square objective function, and the objective function expression is as follows: ; Wherein n calc is a theoretical refractive index, n exp，k is an experimental refractive index of the kth state point, k=1, 2, …, N, and N is the total number of thermodynamic state points.

[0013] The application provides the gas impurity concentration in-situ detection method based on the refractive index gas temperature measurement method, wherein the density of the mixed gas is solved through a virial state equation, and the virial state equation expression is as follows: Wherein, ρ is the density of the mixed gas, R is a gas constant.

[0014] The in-situ detection method for gas impurity concentration based on the refractive index gas temperature measurement method provided by the application further replaces the refractive index measurement with the measurement of the change of dielectric constant or magnetic permeability to detect the impurity concentration.

[0015] The in-situ detection method for gas impurity concentration based on the refractive index gas temperature measurement method provided by the application, the thermodynamic state is a low-temperature environment, the temperature T < 25K, and the mole fraction of each component satisfies the normalization condition .

[0016] The in-situ detection method for gas impurity concentration based on the refractive index gas temperature measurement method provided by the application, the experimental refractive index is obtained by a microwave resonant cavity refractive index measurement system or an optical resonant cavity measurement system.

[0017] The in-situ detection method for gas impurity concentration based on the refractive index gas temperature measurement method provided by the application, comprising: measuring the experimental refractive index of a mixed gas under a known thermodynamic state; constructing a multicomponent mixed gas virial coefficient model containing a cross interaction term; calculating the theoretical refractive index of the mixed gas based on the virial coefficient model; minimizing the residual error between the theoretical refractive index and the experimental refractive index by using a nonlinear optimization algorithm to solve the mole fraction of each component, thereby realizing the in-situ detection of the gas impurity concentration; the application realizes the in-situ and high-precision detection of the gas impurity concentration by the innovative method based on the refractive index measurement and the virial coefficient model, which firstly measures the experimental refractive index of the mixed gas to avoid the cumbersome operation of the traditional sampling analysis, and can reflect the real state of the gas in the low-temperature environment in real time; the theoretical refractive index is calculated by introducing the multicomponent virial coefficient model, which can accurately characterize the interaction between gas molecules, thereby improving the detection accuracy, especially suitable for the analysis of trace impurities; the difference between the experimental and theoretical refractive indices is minimized by using the optimization algorithm, which realizes the nondestructive solution of the impurity concentration without consuming or removing the gas sample, and this universal design is suitable for processing single or multiple impurity scenarios. BRIEF DESCRIPTION OF DRAWINGS

[0018] In order to more clearly illustrate the technical solutions of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and those skilled in the art can also obtain other drawings according to these drawings without creative labor.

[0019] Figure 1 is a flow chart of the in-situ detection method for gas impurity concentration based on the refractive index gas temperature measurement method provided by the embodiment of the present application.

[0020] Figure 2This is a schematic flowchart of an in-situ detection method for gas impurity concentration based on refractive index gas thermometry provided in an embodiment of the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0022] The following is combined Figures 1-2 This invention describes an in-situ detection method for gas impurity concentration based on refractive index gas thermometry.

[0023] This invention provides an in-situ detection method for gaseous impurity concentration based on refractive index gas thermometry, comprising the following steps: Step S1: Under known thermodynamic conditions, measure the experimental refractive index of the gas mixture.

[0024] Specifically, in a low-temperature constant-temperature environment, a microwave resonant cavity refractive index measurement system or an optical resonant cavity measurement system is used to measure the refractive index of a resonant cavity. Different thermodynamic state points (in Experimental measurement of the refractive index of a gas mixture Experimental refractive index The calculation formula is: in These are the resonant frequencies under vacuum and pressure conditions, respectively. The effective compression factor.

[0025] Step S2: Construct a virial coefficient model for a multi-component mixed gas containing cross-interaction terms.

[0026] Step S3: Calculate the theoretical refractive index of the mixed gas based on the virial coefficient model.

[0027] Step S4: Minimize the residual between the theoretical refractive index and the experimental refractive index using a nonlinear optimization algorithm to obtain the mole fraction of each component, thereby achieving in-situ detection of gaseous impurity concentration.

[0028] As can be seen from the above scheme, this invention achieves in-situ, high-precision detection of gas impurity concentration through an innovative method based on refractive index measurement and virial coefficient model. This method first avoids the cumbersome operation of traditional sampling analysis by measuring the experimental refractive index of the mixed gas, and can reflect the real state of the gas in a low-temperature environment in real time. By introducing a multi-component virial coefficient model to calculate the theoretical refractive index, this method can accurately characterize the interaction between gas molecules, thereby improving the detection accuracy, especially suitable for the analysis of trace impurities. By using an optimization algorithm to minimize the difference between the experimental and theoretical refractive indices, this method achieves non-destructive solution of impurity concentration without consuming or removing the gas sample. This universal design is applicable to handling single or multiple impurity scenarios.

[0029] In this embodiment, in step S1, the number of thermodynamic state points is one or more; when detecting a single impurity, one thermodynamic state point is selected; when detecting multiple impurities, multiple thermodynamic state points covering different temperature ranges are selected, and the differences in the temperature dependence of the virial coefficient of different impurities are used for differentiation.

[0030] In other words, when detecting a single impurity, there is only one unknown variable in the gas mixture, namely the mole fraction of the impurity. A single thermodynamic state point can provide a set of experimental refractive index data. Combined with the virial coefficient model, the impurity concentration can be accurately deduced through a nonlinear optimization algorithm without the need for additional state point measurements. This simplifies the operation process, reduces detection time, and achieves efficient detection.

[0031] When detecting multiple impurities, there are multiple unknown variables in the gas mixture, namely the mole fraction of each impurity. The constraints provided by a single state point are insufficient to distinguish the contribution of different impurities to the refractive index. Therefore, it is necessary to select multiple state points that must cover different temperature ranges so that the characteristics of each impurity are differentiated in different temperature ranges, forming multiple sets of independent constraint equations, which provide sufficient basis for solving the concentration of multiple impurities at the same time.

[0032] On the one hand, the single-state-point design for a single impurity scenario avoids redundant measurements, and selecting the temperature range with the greatest difference between the impurity and the main gas virial coefficient further improves detection sensitivity. On the other hand, the multi-temperature-range state-point design for multiple impurity scenarios can adapt to mixed scenarios of any number of impurities (such as He-4 containing He-3, Ar, and Ne simultaneously) simply by adjusting the temperature distribution of the state points, without needing to design a dedicated detection scheme for specific impurity combinations. Simultaneously, the multi-temperature-range state points provide rich data for virial coefficient models with cross-action terms, which can more fully constrain model parameters, reduce computational uncertainties caused by higher-order cross-actions, further improve the accuracy of solving for multiple impurity concentrations, and allow the entire detection method to maintain stable high-precision detection performance in both single-impurity and multi-impurity scenarios.

[0033] Thus, due to the difference in the sensitivity of molecular interaction between different impurities and the main gas, and between impurities, for example, the virial coefficient of He-3 in the low temperature range (such as T<25K) is quite different from that of Ar, Ne and other inert gases. The quantum effect of He-3 will cause the virial coefficient to fluctuate rapidly with temperature, while the polarizability of Ar and Ne will make the virial coefficient change more gently. By setting state points in different temperature ranges, the different characteristics can be fully displayed, and through cross-validation of multiple data sets, the contribution of different impurities can be effectively separated, avoiding the confusion caused by the superposition of the influence of multiple impurities on the concentration solution.

[0034] In some embodiments, the mixed gas in step S2 includes one main gas and at least one impurity. The main gas is He-4, and the impurity is one or more of He-3, Ar, and Ne. For example, the mixed gas is composed of four components, wherein component 1 is the main gas, such as He-4, component 2 is He-3, component 3 is Ar, and component 4 is Ne. ( ) is the impurity to be detected (such as He-3, Ar, Ne, etc.).

[0035] The mole fraction of each component is defined as , and satisfies the normalization condition: wherein, is the mole fraction of the i-th component. i

[0036] In this way, the low-temperature environment can amplify the differences between different components, especially the virial coefficient differences between isotopic impurities and conventional inert gas impurities. For example, He-3 as a quantum gas has more significant quantum effects of intermolecular interaction in the low-temperature range (usually T<25K), which is significantly different from the virial coefficient variation of He-4. The difference in polarizability between Ar, Ne and the main gas can also be more clearly reflected through the changes in density and refractive index at low temperatures, thereby greatly improving the detection sensitivity and ensuring that the detection result can directly reflect the real state of the gas in the scene.

[0037] The mole fraction represents the proportion of each component in the mixed gas. The sum of the proportions of all components must be 1 (without other components missing), and the proportion cannot be negative. This constraint ensures that the final output of the impurity concentration result has practical reference value.

[0038] In step S2, a multi-component mixed gas virial coefficient model including cross-interaction terms is constructed, including: according to the statistical mechanics mixing rule, a function relationship between the macroscopic physical parameters of the mixed gas and the component concentration x is established.

[0039] ​​In some embodiments, the multi-component mixed gas virial coefficient model includes a mixed magnetic virial coefficient and a first dielectric virial coefficient, both of which adopt a linear mixing rule.

[0040] Specifically, the expression of the mixed magnetic virial coefficient is: wherein, is the magnetic susceptibility of the m-th pure component, m is the number of gas types, is the molar fraction of the m-th component. i The expression of the first dielectric virial coefficient is:

[0041] wherein, is the first dielectric virial coefficient of the m-th pure component, m is the number of gas types, is the molar fraction of the m-th component. i

[0042] In some embodiments, the multi-component mixed gas virial coefficient model includes a high-order dielectric virial coefficient, a second density virial coefficient, a third density virial coefficient, and a fourth density virial coefficient, which respectively represent dielectric high-order interaction and two-body, three-body, and four-body molecular interaction.

[0043] Specifically, the expression of the high-order dielectric virial coefficient is: wherein, xi, xj are the molar fractions of the m-th component, i, j is the cross dielectric virial coefficient of the components and i j

[0044] The second density virial coefficient (representing two-body interaction): wherein, is the pure substance virial coefficient, is the cross virial coefficient, representing the interaction between different molecules, such as He-4 and Ar interaction.

[0045] The third density virial coefficient (representing three-body interaction): The fourth density virial coefficient (representing four-body interaction): ​​​​​​Thus, the mixed magnetic virial coefficient represents the macroscopic magnetization characteristics of the mixed gas, the first dielectric virial coefficient reflects the basic dielectric characteristics of the mixed gas, and the essence of the two is the macroscopic superposition of the inherent physical properties of each single component in the mixed system. The magnetization , the basic dielectric characteristics of the single component are inherent parameters of the substance itself and are not affected by the mixing ratio. Therefore, using the linear mixing rule is an objective physical description of the basic magnetic and dielectric characteristics of the mixed gas, avoiding the model approximation error brought by the complex mixing rule. On the one hand, the linear mixing rule does not need to introduce additional fitting parameters or empirical correction terms, and only needs to know the and basic data of each pure component. The corresponding parameters of the mixed system can be directly calculated by the component mole fraction xi , which greatly simplifies the model calculation complexity and reduces the calculation amount of subsequent iterative solution, providing support for the real-time of detection. On the other hand, the linear rule has strong universality. Whether the main gas and impurities are isotopic combinations such as He-4 and He-3, or different inert gas combinations such as Ne and Ar, as long as the basic physical parameters of the single component are obtained, the rule can be directly applied to construct the model without adjusting the mixing logic for specific gas combinations, thereby enhancing the application range of the entire detection method.

[0046] In this embodiment, the cross interaction term includes a binary cross virial coefficient, a ternary cross virial coefficient, and a quaternary cross virial coefficient, which respectively represent the binary, ternary, and quaternary interactions between different molecules.

[0047] Specifically, in a multi-component mixed gas, the interaction between molecules not only exists between molecules of the same component, such as the main gas and the main gas, and the impurities and the impurities, but also exists between molecules of different components, such as He-4 and He-3, and He-4 and Ar, which are also key factors affecting the macroscopic physical characteristics of the gas, such as density and refractive index. The binary cross virial coefficient describes the pairwise interaction between two different molecules, which is the basic form of cross-component molecular interaction; the ternary cross virial coefficient (A Cijk, i, j, k is not completely the same) represents the synergistic interaction when three different molecules exist at the same time; and the quaternary cross virial coefficient (A Dijks, i, j, k, s is not completely the same) further covers the joint interaction between four different molecules, which is suitable for more complex multi-component mixing scenarios. These three types of coefficients completely cover different levels of cross-component molecular interactions and are an objective reflection of the real motion law of mixed gas molecules.

[0048] Traditional ideal mixing models or simplified models typically only consider interactions between molecules of the same component, neglecting cross-component interactions. This leads to discrepancies between theoretical calculations and actual gas properties in trace impurity detection scenarios, as the interactions between the main gas and impurity molecules are not characterized, ultimately affecting the accuracy of concentration calculations. In contrast, the two-body cross-virial coefficient in this invention serves as a fundamental form of cross-component molecular interaction, covering most scenarios dominated by cross-component interactions. Three-body and four-body cross-virial coefficients are designed for special conditions such as low temperature and high pressure, where intermolecular distances are smaller and the probability of simultaneous multi-molecule interactions is significantly increased. Since the influence of higher-order cross-interactions on gas density and refractive index is not negligible, their inclusion makes the model more realistic and avoids calculation errors caused by higher-order interactions. Furthermore, the linearity rules of these three types of coefficients complement those of the mixed magnetic virial coefficient and the first dielectric virial coefficient, ensuring both high efficiency in calculating basic properties and accurate characterization of complex interactions.

[0049] This setup offers several advantages. First, it significantly improves detection accuracy. By fully characterizing the interactions between different molecules at various levels, it greatly enhances the alignment between the theoretical refractive index calculation and experimental measurements, enabling subsequent residual optimization algorithms to accurately infer trace impurity concentrations. Second, it adapts to complex multi-component scenarios. When a gas mixture contains multiple impurities, such as He-4 containing He-3, Ar, and Ne simultaneously, the interactions between different impurities and the main gas, as well as between impurities themselves, can be characterized by corresponding coefficients. This eliminates the need to adjust the model for specific impurity combinations, enhancing the method's versatility. Furthermore, it adapts to specific operating conditions, particularly in applications like cryogenic metrology and quantum standard reproduction, typically in low-temperature environments (T < 25 K) where higher-order interactions are more pronounced. The presence of these three types of coefficients allows the model to stably adapt to these conditions, avoiding detection distortion caused by environmental changes.

[0050] In this embodiment, the nonlinear optimization algorithm is either the Levenberg-Marquardt algorithm or the simplex method. The residuals are calculated using a least-squares objective function, the expression of which is: in n calc Theoretical refractive index, n exp，k Let be the experimental refractive index of the k-th state point, where k = 1, 2, ..., N, and N is the total number of thermodynamic state points.

[0051] That is, using nonlinear optimization algorithms such as the Levenberg-Marquardt algorithm or the simplex method, under constraints... and The following solution makes F(x) Minimum vector This refers to the concentration of each impurity component.

[0052] Further, the density of the mixed gas is solved by the virial state equation, and the expression of the virial state equation is: wherein, ρ is the density of the mixed gas, R is the gas constant.

[0053] Theoretical calculation of the refractive index is calculated by the following formula: In some embodiments, the refractive index measurement can also be replaced by measuring the change of the dielectric constant or the magnetic permeability to detect the impurity concentration, and the detection principle is consistent with the refractive index detection, which is not described here.

[0054] The practical application of the method is described below with a specific example, and the working gas is He-4, and the impurity to be detected is only He-3, and other heavy atomic impurities such as Ne and Ar have been completely removed by a cold trap.

[0055] Step S10: assuming that the mole fraction of He-3 is , then the mole fraction of He-4 is (1- ). Since only a single unknown is involved, only one specific thermodynamic state point needs to be measured, for example, the temperature range of T <25K is selected, at which time the virial coefficient difference between He-3 and He-4 is the largest, and the sensitivity is the highest.

[0056] At a temperature and a pressure , the experimental refractive index is measured.

[0057] Step S20: constructing a multi-component mixed gas virial coefficient model containing cross interaction terms.

[0058] The above general summation formula is expanded for a binary system, and the virial coefficients of He-3 and He-4 are both given high-precision ab initio calculation values: (1) Mixed magnetic virial coefficient : (2) First dielectric virial coefficient: (3) Second dielectric virial coefficient: (4) The second density virial coefficient: where is the pure component coefficient, is the He-4 and He-3 cross coefficient.

[0059] It is noted that for very low concentration impurities ( ), term can be neglected, and the model can be further simplified to a linear approximation.

[0060] (5) The third density virial coefficient: (6) The fourth density virial coefficient: Reference Figure 2 is further described the working process.

[0061] 1. The unknown to be solved: the mole fraction x of He-3 in He-4 mixed gas, by iteratively adjusting the trial value of x, the deviation between the theoretical refractive index and the experimentally measured refractive index is minimized, and finally x that meets the accuracy requirement is obtained.

[0062] 2. Initialization phase Parameter and range setting According to the actual application scene, the value range of x is set as , that is, the impurity content of He-3 is 0~100ppm, covering the typical range of trace impurities in high-purity gas.

[0063] Set the error threshold of convergence criterion , which can be 10 -8 -10 -9 , corresponding to ppb level detection accuracy, which can be adjusted according to actual needs.

[0064] Measured parameters: the experimental refractive index of the mixed gas is obtained in advance by the refractive index measurement system n exp (one-time in-situ measurement can be obtained, without extracting gas samples).

[0065] Fixed parameters: pure component virial coefficient of He-4 and He-3, thermodynamic state parameters (pressure p, temperature T, known constant value), gas constant R, etc.

[0066] 3. Iterative solution phase (bisection method or Newton iteration method) Initialization: set the initial guess range .

[0067] Iteration loop: take the trial value The mixture parameter is calculated by using the above formula, and the virial state equation (9) is used to solve the mixture gas density , and then the theoretical refractive index is calculated by equation (8) . A nonlinear fitting method is used to calculate the adjustment , until (error tolerance).

[0068] The output result: the of the He-3 impurity content detected.

[0069] Through the above steps, without extracting the gas sample, the isotope abundance of He-3 in He-4 gas can be accurately calculated by using one refractive index measurement.

[0070] Similarly, in the multi-impurity scene, formulas (1)-(10) can be used to complete the component analysis of the known gas.

[0071] The present application realizes direct measurement of refractive index in the original thermodynamic environment of the gas p, T , without the need to extract samples or damage the system seal. This design fundamentally avoids the problems of gas state distortion, system pollution or sample loss caused by sampling in traditional offline detection (such as GC-MS), and is suitable for low-temperature measurement, quantum standard reproduction and other scenes with extremely high requirements for the stability of closed systems. It can not only guarantee the continuity of the experimental environment during the detection process, but also truly reflect the impurity concentration of the gas in the original state, avoiding the detection distortion caused by the gas deviating from the original working condition after sampling. Secondly, by constructing a multi-component mixed gas virial coefficient model containing cross interaction terms, the complex interaction between gas molecules is truly restored, and the double, triple and multi-body cross interaction between the main gas and impurities, and impurities is accurately characterized. Overcome the defects of traditional ideal mixing model ignoring the interaction between molecules, making the calculation of theoretical refractive index more in line with the actual physical properties of the gas. ​The refractive index, which is sensitive to the concentration change, is converted into the accurate solution of the concentration by minimizing the theoretical and experimental refractive index residuals through a nonlinear optimization algorithm, thereby minimizing the calculation error to the greatest extent; when detecting a single impurity, only one thermodynamic state point is needed to provide sufficient constraint conditions; when detecting multiple mixed impurities, by selecting multiple state points covering different temperature ranges, the concentration of multiple components can be simultaneously solved by using the temperature dependence difference of the virial coefficients of different impurities; this design does not need to design exclusive detection modules for different impurities, and can cope with the single isotope impurity scenario of He-4 containing He-3, and can also adapt to the multi-impurity mixed scenario of Ne containing He and Ar, thereby improving the applicability and flexibility of the method; at the same time, the detection process of the method does not need time-consuming steps such as sample pretreatment, offline transmission, chemical reaction analysis, etc., and is only physical parameter measurement (refractive index) and mathematical iterative calculation (virial coefficient model, optimization algorithm), the refractive index measurement can be completed in real time, and the convergence speed of common optimization algorithms such as Levenberg-Marquardt algorithm is extremely fast (usually milliseconds to seconds), which can quickly output the impurity concentration result; the method does not depend on the exclusive chemical or physical characteristics of a specific gas, as long as the basic data of the virial coefficient of each component can be obtained, the concentration can be solved through model iteration, whether it is the combination of the main gas and the isotope impurity, or the combination of the main gas and multiple inert gas impurities, the method can realize accurate detection, so that it can cover the high-purity gas impurity detection needs of multiple fields such as low-temperature physics, primary temperature measurement, quantum standard reproduction, etc.

[0072] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement to part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for in-situ detection of gaseous impurity concentration based on refractive index gas thermometry, characterized in that, Includes the following steps: The experimental refractive index of a gas mixture is measured under known thermodynamic conditions. Construct a virial coefficient model for a multi-component mixed gas that includes cross-interaction terms; The theoretical refractive index of the mixed gas was calculated based on the virial coefficient model. By minimizing the residual between the theoretical refractive index and the experimental refractive index using a nonlinear optimization algorithm, the mole fraction of each component is obtained, thus enabling in-situ detection of gaseous impurity concentration.

2. The in-situ detection method for gas impurity concentration based on refractive index gas thermometry according to claim 1, characterized in that, The mixed gas comprises a main gas and at least one impurity.

3. The in-situ detection method for gas impurity concentration based on refractive index gas thermometry according to claim 2, characterized in that, The number of thermodynamic state points is one or more; when detecting a single impurity, one thermodynamic state point is selected; when detecting multiple impurities, multiple thermodynamic state points covering different temperature ranges are selected.

4. The in-situ detection method for gas impurity concentration based on refractive index gas thermometry according to claim 1, characterized in that, The multi-component mixed gas virial coefficient model includes a mixed magnetic virial coefficient and a first dielectric virial coefficient, both of which adopt a linear mixing rule.

5. The in-situ detection method for gas impurity concentration based on refractive index gas thermometry according to claim 1, characterized in that, The multi-component mixed gas virial coefficient model includes higher-order dielectric virial coefficients, second-density virial coefficients, third-density virial coefficients, and fourth-density virial coefficients, which respectively characterize higher-order dielectric interactions and two-body, three-body, and four-body molecular interactions.

6. The in-situ detection method for gas impurity concentration based on refractive index gas thermometry according to claim 1, characterized in that, The cross-interaction terms include two-body cross-virial coefficients, three-body cross-virial coefficients, and four-body cross-virial coefficients, which respectively characterize two-body, three-body, and four-body interactions between different molecules.

7. The in-situ detection method for gaseous impurity concentration based on refractive index gas thermometry according to claim 1, characterized in that, The nonlinear optimization algorithm is either the Levenberg-Marquardt algorithm or the simplex method. The residuals are calculated using a least-squares objective function, the expression of which is: ； Where n calc n is the theoretical refractive index. exp，k Let be the experimental refractive index of the k-th state point, where k = 1, 2, ..., N, and N is the total number of thermodynamic state points.

8. The in-situ detection method for gas impurity concentration based on refractive index gas thermometry according to claim 1, characterized in that, The density of the gas mixture is solved using the virial equation of state, which is expressed as follows: in, ρ The density of the mixed gas, R is the gas constant.

9. The in-situ detection method for gas impurity concentration based on refractive index gas thermometry according to claim 1, characterized in that, Impurity concentration can also be detected by measuring changes in dielectric constant or permeability instead of refractive index.

10. The in-situ detection method for gas impurity concentration based on refractive index gas thermometry according to claim 1, characterized in that, The experimental refractive index was obtained using a microwave resonant cavity refractive index measurement system or an optical resonant cavity measurement system.

Images