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There are many places in industrial settings where gas flow measurement is required; typical applications include air, gas, natural gas, chlorine, oxygen, flare gas, vehicle exhaust, and so on. In situations where combustion control is necessary, gas flow measurement is crucial for the optimal control of the air/fuel ratio. The amount of air supplied for combustion directly affects its stability and efficiency. In the hydrocracking processes of the petrochemical industry, measuring and controlling the hydrogen flow rate is of great practical significance for optimizing operations and improving efficiency. With the rapid development of China’s industry and the strong push for emerging energy sources driven by environmental protection requirements, gas metering is receiving increasing attention. However, the issue of gas flow measurement is quite prominent at present. For example, large-diameter, high-flow gas flowmeters have many problems ； The metering of mixed gases with significant variations in parameters such as temperature, pressure, and composition is also a major challenge that needs to be addressed urgently. 1.1 Characteristics of mixed gases Mixed gases are commonly used media in industrial settings; natural gas, gas, flare gas, and boiler flue gas are all typical examples of mixed gases. Mixed gases generally have the following characteristics: a. Severe contamination. Mixed gases generally contain some impure components; for example, gas contains impurities such as coal tar, dust, and water ； The flue gas contains fly ash. b. Variable components. The components of the gas mixture undergo certain changes, exhibiting time-varying characteristics. For example, coal gas contains various components such as CO2, O2, H2, CO, and CH4. Depending on changes in the production process or differences in raw material composition, the composition of coal gas can vary. For example, flare gas contains components such as hydrocarbons, hydrogen, hydrogen sulfide, carbon dioxide, and nitrogen; changes in the refining process or valve leaks can also cause variations in the relative percentages of these gases in the flare gas. c. Changes in temperature and pressure. For example, the temperature of torch gas varies greatly, ranging from low temperatures in the low tens of degrees below zero to high temperatures of three to four hundred degrees. Changes in temperature and pressure of the gas mixture under test can lead to significant measurement errors. Therefore, it is much more reasonable to measure the mass flow rate of the mixed gas than its volume flow rate. d. The range of flow variation is large. Mixed gases such as natural gas, gas, and flare gas all have a wide range of flow rates. For example, the flow velocity of the flare gas in a normally operating refinery is usually low; the typical range for such flow velocities at low rates is 0.01–15 m/s. However, in the event of an accident, the flow velocity of the flare gas can reach 60 m/s within a short period of time. A similar situation exists with natural gas and coal gas, as the gas flow rate during peak usage times can be more than 20 times higher than it is during off-peak times. 1.2 Discussion on gas flow measurement methods: Most of the existing gas flow measurement methods have certain shortcomings to varying degrees when measuring gas flow, making it difficult to resolve the issues associated with gas flow measurement perfectly. Gas flow measurement methods must be realized through specific flow meters. The following analyzes common gas flow meters and the problems that arise in gas flow measurement. 1.2.1 Vortex flow meter The vortex flow meter is a new type of flow meter that was developed in the 1970s, and it is now among the commonly used flow meters. It is widely used to measure the flow rate of gases, liquids, and vapors. Vortex flowmeters have seen rapid development, particularly in terms of signal detection methods and signal processing. There are several advantages to using vortex flowmeters: for example, they are easy to install and cause minimal pressure loss ； A wide range of fluids can be measured, such as liquids, gases, and steam ； Relatively high accuracy ； The measurement range is wide, ranging from 10:1 to 20:1 ； Within a certain range of Reynolds numbers, the output signal is not affected by the fluid properties (density, viscosity) or its composition; in other words, the instrument coefficient depends only on the shape and dimensions of the vortex generator and the pipe ； It only needs to be calibrated in one typical medium, yet is applicable to various media. However, vortex flowmeters also have some drawbacks in practical use: they are not suitable for measuring fluids with low Reynolds numbers ； The stability of vortex separation is related to the distortion of flow velocity distribution and the rotating flow; therefore, a sufficiently long straight pipe section should be provided or a flow rectifier should be installed based on the different types of resistance elements located upstream ； Vortex flowmeters that use force-sensitive detection methods are sensitive to mechanical vibrations in pipelines, and therefore are not suitable for use in environments with strong vibrations ； Compared to turbine flowmeters, it has a lower coefficient of performance and lower resolution. When a vortex flow meter is used for gas measurement, pipeline vibrations caused by pressurization equipment, the impact force of the gas within the pipeline, as well as the random pulsating pressures of the gas, can all affect the flow measurement. Moreover, in practical applications, it is generally difficult to maintain a flow velocity of over 5 m/s, which results in a very noticeable undercounting issue with vortex flow meters at low flow rates. 1.2.2 Differential pressure flow meters: Differential pressure flow meters calculate flow rate based on the differential pressure generated by a throttling element installed in the pipeline, as well as parameters such as known fluid properties, the characteristics of the throttling element, and the geometric dimensions of the pipeline. Its usage ranks first among flow meters. In recent years, with the widespread use of various new types of flowmeters, the market share of differential pressure flowmeters has gradually declined; however, they remain the most important type of flowmeter to date. Differential pressure flowmeters are widely used in gas flow measurement and represent the mainstream type of flowmeter for measuring coal gas and natural gas at present. According to recent surveys, among gas flow measurement instruments, standard orifice plates account for about 55% internationally and about 80% in China. A differential pressure flow meter consists of a primary device and a secondary device. Differential pressure flowmeters are usually classified by the type of throttling element, such as orifice plate flowmeters, venturi flowmeters, and average velocity tube flowmeters. The throttling element of differential pressure flowmeters (especially the standard-type throttling element) is quite universal and recognized by international standards organizations. The experimental research on standard orifices for differential pressure flowmeters is international in scope; it is difficult for other types of flowmeters to achieve such depth and breadth. The standard differential pressure flow meter is the only type of flow meter that can be put into use without the need for calibration using actual flow. Differential pressure flow meters also have certain limitations in use: their measurement repeatability and accuracy are at a medium to low level, and it is difficult to further improve them ； The measurement range is relatively narrow; it is generally only 3:1 to 4:1 ； It cannot be used in situations with large fluctuations in flow rate. Some studies have also proposed methods to expand the measurement range of differential pressure flow meters, but the requirements for on-site installation are high ； Pressure guiding pipes are prone to faults such as leaks, blockages, freezing, and signal distortion ； High pressure drop. Differential pressure flowmeters are not suitable for dirty mixed gases such as coal gas, natural gas, and flue gas. The main reasons are as follows: a. Coal gas and natural gas experience peak and low usage periods, resulting in large fluctuations in flow rates; the low range ratio of differential pressure flowmeters leads to significant errors in such applications. In practical applications, connecting branch pipes in parallel to the main pipe is generally employed to expand the rangeability of differential pressure flow meters. However, this approach complicates the metering system, increases investment costs, and raises maintenance requirements. b. Mixed gases such as gas, natural gas, and flue gas contain dirty impurities, which often lead to problems such as blockages in the pressure guiding pipes and changes in the characteristics of the throttling elements. To this end, some companies have developed washable orifice plates that are easy to clean; these are cleaned periodically or irregularly to ensure the proper operation of the instruments and their measurement accuracy. However, in actual practice, it remains difficult to resolve various problems caused by dirt and contamination. c. High pressure loss, which is not conducive to the pipeline transportation of gases. Furthermore, differential pressure flow meters cannot be used with oxygen fluids or in low-pressure applications. 1.2.3. Rotameter A rotameter, also known as a float flowmeter, is a type of variable-area flowmeter. Rotary flow meters have a simple structure; their usage is second only to that of differential pressure flow meters, and they play a crucial role in measuring very small flow rates. Single-rotor flow meters have drawbacks such as small pipe diameters and numerous installation restrictions. Rotary flowmeters have low measurement accuracy and require calibration using real gases; they can only be used in applications with modest requirements (accuracy below grade 2.5). Gases such as coal gas and natural gas often encounter issues related to trade settlement; thus, a certain level of measurement accuracy must be ensured. Moreover, variations in the composition of mixed gases can affect the output signal of flow meters. Therefore, rotameter are not well-suited for applications involving mixed gases, large pipe diameters, or situations where high measurement accuracy is required. 1.2.4 Turbine flow meters A turbine flow meter consists of a sensor and a conversion display unit; the sensor uses a multi-blade rotor to detect the average flow velocity of the fluid, thereby determining the flow rate. The flow velocity of the rotor can be detected using methods such as magnetic induction and photoelectric detection, and is then displayed, transmitted, and recorded by downstream devices. Turbine flow meters are widely used for measuring petroleum, organic liquids, inorganic liquids, liquefied gases, natural gas, coal gas, and cryogenic fluids. Abroad, turbine flowmeters are widely used for trade settlement at transfer and distribution stations for liquefied petroleum gas, refined oil, light crude oil, etc., as well as at the starting and ending points of large-scale crude oil transmission pipelines. In Europe and the United States, turbine flowmeters are the second-most commonly used gas metering devices after orifice plate flowmeters. Turbine flowmeters have the following characteristics: high accuracy, generally ranging from 0.5% to 0.2% ； The measurement range is moderate, with the maximum to minimum flow ratio typically ranging from 6:1 to 10:1 ； Good repeatability ； Low pressure loss ； Digital signal output ； Easy to install and maintain. The limitations of turbine flow meters are: they cannot maintain their calibration characteristics over the long term, and require regular calibration ； Generally not suitable for flow measurement of high-viscosity media ； Fluid properties (density, viscosity) have a significant impact on flow characteristics ； Flow velocity distribution and distortion have a significant impact on flow rate ； High requirements are placed on the cleanliness of the medium being tested. It can be seen that although turbine flowmeters have high accuracy, their range is relatively limited; they are prone to contamination and wear, and the manufacturing cost of large-diameter turbine flowmeters is quite high. Therefore, it holds a significant role in the measurement of clean gas flow rates at medium and small pipe diameters (under DN300), but it is not suitable for use with dirty gases such as coal gas and natural gas. 1.2.5. Ultrasonic flow meters: Ultrasonic flow meters are instruments that measure the volumetric flow rate of a fluid by detecting the effect of the fluid flow on an ultrasonic beam. It has no pressure loss and is one of the flow meters that have seen rapid development in recent years; it boasts significant advantages in measuring large-diameter flows. Ultrasonic flow meters used in closed pipelines can be classified according to their measurement principles into: time-of-flight method, Doppler effect method, beam deflection method, correlation method, and noise method. The use of ultrasonic flowmeters began in the 1990s. Thanks to their various advantages such as high measurement accuracy, a wide range of measurement capabilities, no pressure loss, and the absence of moving parts, they have become popular among users and are used for measuring gas flow. To date, 12 countries including the United States, the Netherlands, and the United Kingdom have approved ultrasonic flowmeters as legal measuring instruments for trade settlements. But it is only suitable for medium to large diameters, and it is expensive. Currently, a small number of users in China use imported ultrasonic flow meters for flow measurement. 1.2.6. Gas gear flow meter: A gas gear flow meter is a type of volumetric flow meter that offers high measurement accuracy and reliability. It does not require straight pipe sections before and after it during installation, and it has a wide measurement range, which can reach 10:1. However, due to structural reasons, when installed, the housing of gas oval gear flow meters cannot withstand various stresses from the pipelines; moreover, the medium must be extremely clean (otherwise the rotating parts are prone to getting stuck). Therefore, its application in mixed gas flow measurement is subject to certain limitations. Additionally, due to their considerable bulkiness, large-diameter oval gear flow meters are rarely used in large-diameter pipelines; instead, they are primarily employed on-site for measuring gas flow rates in small-diameter pipes. Some other positive displacement flow meters, such as wet flow meters and Roots flow meters, also have difficulty being used for mixed gases due to installation limitations. 1.2.7. Thermal Gas Mass Flow Meter A thermal gas mass flow meter is a device that measures gas flow by utilizing the principle of heat exchange; in other words, it measures flow based on the heat exchange between the flowing gas and a heat source. In the 1960s, the United States first developed thermal gas flow meters for the aerospace industry; subsequently, they saw significant development in the semiconductor industry. Thermal gas mass flow meters have the following characteristics: they can measure very low flow rates of tiny volumes of fluid ； No moving parts, high reliability ； The pressure loss is very small, almost negligible ； Direct measurement of mass flow, no pressure or temperature correction required ； Electrical signal output, high output value ； Very high range ratio (1000:1) ； The price has little to do with the pipe diameter, and it is easy to install ； Good reproducibility. Currently, thermal gas mass flow meters are widely used for measuring gas flow rates in various industrial fields, such as natural gas flow measurement, gas metering, air flow measurement, flare gas flow measurement, hydrogen flow measurement, oxygen flow measurement, the automotive industry (for measuring vehicle exhaust), CEMS systems, the healthcare sector (for measuring oxygen and medication flow rates), the energy industry (for combustion air control), heating and ventilation systems, and public services (for measuring the flow rate of gases such as chlorine and ozone). 1.3. Measurement of gas mass flow rate As can be seen from the previous analysis of flow measurement instruments, most flow meters measure volumetric flow rate. In industrial metering, the temperature, pressure, and composition of the medium are constantly changing, which results in significant errors in the measurements of volumetric flow rate, rendering such measurements meaningless. In these applications, measuring the mass flow rate of the medium is far more practical than measuring its volume flow rate. These scenarios include ratio and quality control in industrial production, material and energy balance, as well as trade settlement. After more than 20 years of exploration and experimentation, mass flowmeters with practical application value have been developed. The common methods for measuring mass flow rate are mainly the indirect method and the direct method. 1.3.1. Indirect mass flow measurement: The indirect method of mass flow measurement is one of the approaches that has been used in industry for a relatively long time. Indirect mass flow measurement methods are widely used in applications where high measurement accuracy is not required, the range of temperature and pressure changes is small, or there is a linear relationship between the medium’s temperature and density. However, for media whose relationship between temperature, pressure, and density is complex, it is difficult to achieve automatic and accurate compensation. At the same time, this measurement method involves the measurement of multiple intermediate parameters, resulting in a large number of measurement steps, which makes it difficult to ensure and improve the accuracy of mass flow measurement. 1.3.2. Direct mass flow measurement: Over the years, direct mass flow measurement methods have given rise to various types of mass flow meters. Some of these mass flow meters are improvements based on volume flow meters. For example, differential pressure mass flow meters composed of orifice plates and constant-flow pumps, twin-turbine mass flow meters made up of two turbines, etc. Due to structural reasons, these flowmeters are difficult to be widely used. Currently, in practical applications, Coriolis mass flow meters are primarily used to directly measure the mass flow rate of liquid phases or multiphase fluids dominated by liquid phases, whereas thermal mass flow meters are mostly used to directly measure the mass flow rate of gases. At present, Coriolis mass flowmeters still have some problems and limitations in application; they are mainly used for measuring single-phase fluids, especially suitable for measuring single-phase liquids. Some studies also suggest that it can be applied to the flow measurement of dense gases, but these research findings have not yet reached a practical level. The thermal gas mass flow meter originated from the “hot-wire anemometer”. As the advantages of thermal measurement technology were recognized, thermal gas flowmeters developed rapidly. Thermal gas flow meters are divided into two types: energy balance type and convection type. Energy-balanced thermal flowmeters are also known as thermal distributed flowmeters or calorimetric flowmeters, while convective flowmeters are based on Kirchhoff’s law regarding the heat dissipation (cooling) effect; they are also referred to as intrusive or inserted flowmeters. Energy-balanced thermal flowmeters are widely used for measuring low flow rates, while convective thermal gas flowmeters are generally used for measuring high flow rates. Convection-type thermal flowmeters are further divided into two types: constant energy type (constant flow) and constant temperature type (constant temperature). Thermal gas flow meters with temperature constancy have a higher response speed compared to those with constant specific energy, and this represents the main development direction for thermal gas flow meters at present. Traditional thermal gas mass flow meters require the gas being measured to be of a single component or with a fixed composition, and they also have relatively strict requirements regarding process conditions. However, several international manufacturers specializing in thermal flowmeters, such as SIERRA in the United States, have developed advanced technologies in this area; their thermal gas mass flowmeters deliver excellent measurement results in applications involving gases with complex process conditions and multiple components mixed together. Moreover, the product can have a service life of up to 10 years with its performance remaining excellent. 1.4. Feasibility analysis of flow measurement methods for mixed gases. As can be seen from the previous analysis, ultrasonic flowmeters and thermal gas flowmeters are more suitable for measuring the flow of mixed gases; however, ultrasonic flowmeters are expensive, making it difficult to deploy them on a wide scale. Thermal gas flow meters are reasonably priced, easy to use, and have certain advantages in measuring mixed gases; therefore, research on thermal gas flow meters holds good prospects. The contact surface between the probe of a thermal gas flow meter and the gas is made of various metals or alloys, which are resistant to corrosion and high temperatures, and whose surfaces can be easily cleaned of dirt. It is generally designed for plug-in installation with ball valves, allowing for the insertion, retrieval, and cleaning of the probe online without interrupting gas flow. This can eliminate the effects caused by contamination in the mixed gas. A thermal gas flow meter measures the mass flow rate of gas directly, and can largely eliminate the effects of changes in gas temperature and pressure. Thermal gas flow meters experience extremely low fluid resistance, with virtually no pressure loss. Thermal flowmeters have a very wide range, making them highly suitable for situations where the flow rate of mixed gases varies significantly.